People get their names from three sources
There is the 4th one too - Names which a person takes a fancy to, or thinks important for their own reasons, and we mustn't forget this one. This category includes default names (often biblical) and nature names, such as those Hippies often chose for their children (Oak, Storm, River etc)
Each of these sources can trump another - a name which has been in the family for generations for the first son might lose out if a new baby is born as the first son of the next generation just as a famous national figure reaches their zenith.
Names are not set in stone until the moment of christening/registration and many a parent has thought that they knew the name of their baby-to-be only to change it after the baby was born.
But for alternate history purposes what we are really interested in here, is a mixture of the second and third instances, with a small mix of the fourth.
To take a modern example, whilst the name Kylie was not unknown prior to her fame (or neither Miss Minogue nor her co-star on Neighbours Kylie Flinker would have borne it), it was not at all common and was in pretty limited use. But when her fame took off, the name Kylie really rocketed in popularity.
It can be more difficult with names that are always there anyway - there are always girls christened Charlotte, and whilst Charlotte Church might have boosted the popularity of the name for a while, it was not so obvious as any individual baby Charlotte might well have been named that anyway - statistically there was a surge, but it was less of a surge in percentage terms as there were always a few Charlottes around, decade after decade.
An example of a name that can be considered in vogue is Jessica, year after year high in the list of new baby names, but never really having someone it is named after. The same goes for the boy's name Jack. Newspapers and celebrity magazines help by letting the public know what celebrities or people who are really famous are naming their children - but did we see a rise in the instance of Daisy Boo, or Buddy Bear? Its a mixture of fame and vogue which names get used the most.
In the past, the availability of celebrity gossip was limited to those who lived in the cities and could afford a newspaper or newsheet. But the names that everyone knew were the royal names, the names of the leading politicians and the names of the leading military commanders of the day.
Added to this, in the cities, would be the names of entertainers of one form or another, quite possibly the names of famous hangmen, notorious criminals and the names that the literate, or semi-literate, saw on advertisement signs - for shops, or stalls or goods.
Alternate History
If the world you are setting your story or timeline is has some significantly different names in its recent past, then expect more of your characters to bear those names.
Example 1 If Charlotte, daughter of King George IV, had not died in childbirth and had become Queen, then both her name and that of her husband, Leopold of Saxe-Coburg, would have been high among the names that new parents considered giving to their children.
Concomittantly, the names of Victoria and of Albert would have been statistically far fewer.
Example 2 If Hitler had never risen to power, the male name Adolf would have been more common in English speaking nations, and there would be one or two amongst your acquaintances
Example 3 Sporting prowess also has its impact; the girls name Shannon took off after the success of the gymnast Shannon Miller, for example. Also in gymnastics, the name Nadia had a miniboost after the success twenty years before of Nadia Comeneci.
Example 4 Even fictional names have their impact. Whilst Bianca Jagger is of course factual, the name Bianca for a modern girls name did not take off until the popularity of the character Bianca on the soap Eastenders, a character ironically probably named in the scriptwriter's mind for Bianca Jagger.
None of these are rules, only observations. Regarding Example 3, one did not notice a boost in popularity in English-speaking countries for either the name Olga in the 1970s, or Lavinia in the 1980s despite the successes of Olga Korbut and Lavinia Milosevici.
Some of it is to do with politics - there would not be many Labour supporters in 1945 who would have named their son Winston after Prime Minister Churchill. Then again, perhaps politicians are always a neutral or a negative - how many Clements were there, named for Attlee or Margarets named for Thatcher? People probably don't consider politicians by and large to be people they should name their children after. It only comes into effect when they decide that they are people they should NOT name their children after - like Adolf Hitler.
Thoughts
I had a great aunt named Olga - I don't know why, nobody seems to know why, not now anyway. She was Welsh on both sides, and her sisters had names that were relatively common in Britain at the time, though largely unheard of now for a baby. But Olga? I think it must have come from the Grand Duchess of that name, the eldest of Tsar Nicholas II's daughters and someone who would have been in the news a lot around the time of her birth, someone with seemingly exotic and glamorous connections. I could be wrong but it fits the time frame, and one can only play 'what ifs' with it - what if Olga Nicolaevna had not lived beyond infancy, would the second daughter of the Tsar, Tatiana have supplied an unusual name for my Welsh great aunt?
For the novelist or creator of timelines, names are not so much a set of rules as a trap to be avoided. Of course people that have babies named after them had their own names IRRESPECTIVE of their own fame, but in many a place where their own name would never have been among the common purview of couples looking for a name for their baby it would not have surfaced.
You can write a timeline in which someone is called Edward or George or John or Paul and set it in any alternate history of the last millennium. But if you had a Leopold in pre-nineteenth century times, or even an Albert, there should be a good reason why the character has that name. For any early modern or later setting the names Charlotte, Elizabeth, Mary and so on would be an easy enough one to accept, but have a Kylie in Elizabethan times, or a Lettuce in modern times and it would not only jar but be anachronistic. Of course, maybe the name Kylie does have medieval origins but if so it would only be in a specific area and only people from there (South Wales maybe?) would be using it. And maybe your timeline has preserved the more outre of Victorian names to the present, but if it has then then there should be a reason why there are Lettuces and Elijahs wandering the streets!
While we can discuss the merits of Kylie, both Lorna and Wendy provide another lesson for the alternate historian - both names were made up by novelists. Before they were coined for the various books (Lorna Doone and Peter Pan), the names did not exist as girls names. If the novels are not written, and certainly before the novels are written, the names would be out of time, outside of logic. A word of caution though - I once thought I had made up a name in a story I wrote, but it turned out after all that Suzette was an acceptable French name. It was Fantasy I wrote and I had used a common root and a common end to create what I thought was an unusual and unknown name, but as both were common it turned out the name had been in use for centuries after all.
I recently read a novel in which a minor character was called Lorna. Its just about in the timeframe where the influence of Lorna Doone could have spread the name, but to an illiterate poor family? Maybe, since once the name Lorna had escaped from the book it would have propagated along many a route into the general public. However, it could be an error - or it could be the result of greater knowledge than "what is commonly known".
Nigella Lawson exists, and I bet if we did a search we would find a couple of things - that the name Samuella is out there, and also that there have been Nigellas and Samuellas around for the last century or more somewhere. The relevance to this and Lorna, is that Lorne is a boy's name (see Lorne Greene), taken one assumes from the Scottish island originally. Now, what is a boy's name often acquires a female form, even if in very rare usage (I've never met a Nigella or a Samuella, for example). One assumes that the author of 'Lorna Doone' got inspiration for the name from somewhere - quite probably the boys' name Lorne. Thus, if he could give it a feminine form as Lorna for his novel, then so too could some families in times past, and even times contemporaneous.
No Rules
Thus I would reiterate again that there are no rules, only guidelines. If you want a medieval Scottish lass called Lorna, then you can justify it. If you want a modern gentleman called Elijah or Jehosophat, then you can probably find a real example, and you can work justification into the timeline. If these names are common, then the timeline needs to explain that. To me, that is the major point - if a name is not usual for the time period, or logical for the timeline, then its use should be explained. People have names that are unusual, or go actively against the grain (River Phoenix, or Daisy Boo Oliver, or Fifi Trixabell Geldof in modern times) but they are explained by the background of those giving the name.
What changes in an alternate history timeline is not so much individual choices but statistical overviews. If Charlotte and Leopold reign happily until the mid nineteenth century and follow the usual pattern of naming children for themselves, then by 1900 there should be a lot of Leopolds in Britain. It doesn't mean that your character should be called Leopold, or even that he cannot be called Albert if you want, only that he should know a couple of people called Leopold amongst his acquaintances, co-workers and friends.
If your story is set in such a time, then a few of the people mentioned should have that name, one by the law of averages should be a character in the story, even if a minor one.
It is of course one of the great failings of authors who are not writing historical fiction, that very very few characters share the same first names. It would be too confusing for readers, or would mean they would have to think... But to someone who writes historical fiction set in the War of the Roses just think of all those characters called Edward, Richard and Henry! Luckily they all had titles and different forms that could be used to distinguish them, they could be referred to as the Prince of Wales or the Duke of York, or the Earl of Richmond, so diluting the names confusion.
But any realistic timeline would have people with the same first name, often in office at the same time. Remember history here - the Thatcherite Normans and Kenneths for example? If your timeline becomes a novel, or if you aim to write an alternate history novel which approaches what novelising a timeline would be like, then you need to duplicate first names. What those names would be would depend on the timeline, but would represent a statistical result - ie in the Charlotte and Leopold world, where the crown passed from Queen Charlotte to her son King Leopold I to his son King Leopold II then by 1910 the British cabinet should have in it, by statistical right, a couple of people whose first name is Leopold.
In conclusion
The popularity and statistical instance of names change according to the specifics of your timeline, but for individuals in most cases it matters less.
Where a name would be highly unusual either because it has not yet come into common use, or because it long ago fell out of common use, then its existence in your story should be explained.
When a statistical overview is taken of your timeline or story there should be more people bearing the names that would be common in that timeline, comparative both to other names, and to OTL.
There ought to be more than one person with the most common first name, even if for the sake of the story, or the reader, the second bearer of the name is not a character so much as a passing mention, or a famous figure in this alternate world.
There should be a spattering of names which reflect a different set of famous people. Whilst these would largely being made up here, the very fact of their being different would be enough to add flavour to a novel, especially if a passing mention of one or two of these non-existent (in reality) people is made.
Many names recur generation after generation, century after century and will not die away, but it is the body of names which supplement these which add colour to the story. Sure you have a load of Johns, Charles, Pauls and Marys in your alternate world, but the addition of some significant Jeremiahs, Adas, Lewis' and Brendas could make all the difference.
A timeline, or novel based on an alternate history, is the sum of its parts. One of those parts needs to be a body of names which reflects the world and society the fiction is set in, and where the statistical report on that world would show a slewing towards an allohistorical perspective.