The idea of allowing players to name any character is interesting, but honestly, it can make the game less memorable in the end. Normally, people aren't interested in customizing names and would prefer fixed ones. I saw a comment from someone who had to name a character, and they just ended up calling her 'the Black one.' They didn’t want to sound offensive, but how else could they refer to the character?
Just having a simple option at the beginning of the game asking whether you want to customize the names or not would do wonders.