Naming the MC, yes, but for any other characters, whatever how relevant to the story they are, this must be purely optional, and handled intelligently.
It's really infuriating to have to name dozens of characters, even more when it's the first thing you've to do when the character appear on the screen and you don't even know who the fuck she is. And don't get me started with the tons of consecutive "this is your [whatever], what is her name".
Ideally, the UI should have a, discreet, "rename" button leading to a page where all the already known girls can be renamed if and when you want to change their name. With a picture of the girl to remember who the fuck she is.
And please, pretty please, if you don't want them to be named "trash number 1", "lazy dev" or "who's that bitch"1, give them a default name, thanks.
1: Those a real names of some characters in games I played. I'm grumpy, what mean that I'm not here to do your job at finding characters' names.