Take the example of India, after the mongol conquest of north India.
The part of mongol empire who conquered India becames the Moghul Empire with a lot of people been indian in ethnicity and the ruler cast been mongol. At that point this is an event that change the name of civ, but once they recover they independence the civ come back with the original name.
Since there are regions of India who don't have been captured and the mongols conquest change religion in actual Pakistan, Kashmyr and BanglaDesh, this regions have gained a sense of culture split to India that don't haven't if they remain Hindus or Budhists, and therefore this bring a dynamic to subcontinent. Compare this with Pundjab with their Hindu/Islam combo religion, but don't want separate of India.
Another example is the muslims bosnians, who convert to Islam by under Turks domination.
When Spain conquered Aztecs they become Mexico.
But in the way around? There are no historical examples. And if Irquois conquest Aztecs?
We can solve these problem only change the names that we know from history, but I think that is useless, since don't bring much more to the game, only a change of names and a sense of a more dynamic game, so why not? Although that I like the idea of a civ conquered by another and remain their ethnicity, and later recover its independence.
To play with certain dates and names more accurate we can play a cenario, since the game it's not a world history cenario.
And by the way that leave the player with less more options and predeterminate situations no matter what the player do.
The game are not historically accurate, so what, only for fun. The idea is you pick up a civ in 4000 BC and stand the test of time trough 2050 AD. It's only this. Otherwise could be there a confusion between game itself and cenarios we can modelling.