Could you please add an option to rename AI cities in a single player game. I love change them to something I can remember better or to refresh the city names to match the nation being played. 

It would be great if AI players occasionally updated their own city names, too.  Not all the time, of course — it might be hard for us to keep up with them — but if they prioritized updating their capital to their current culture's capital, and every ten turns or so updated a name to match their current culture, I agree, that'd be nice for immersion.

Maybe if they prioritized updating their capital and their smallest/weakest cities, so behemoths like Mohenjo-Daro could remain iconic?

In solo games, it should be the player's decision.

Maybe even at culture change all the cities names should be updated. It just seems strange having ancient city names in the later ages under completely different cultures. 

Maybe it is something that happens as part of refreshing the city, I forget what the build option is called, but then I'd like to see that AI doing that 1 turn update on cities as well.