Yes, Thor is the Odinson's name, but there's nothing stopping Thor from letting her use his name, particularly when he views himself as both unworthy of the hammer and unworthy of the respect, responsibility, and adulation that comes with it. Which is basically what he did.

There's also the fact that no one knew who the new Thor was so what do you call her? "hey you with the hammer?"

I can see where people are coming from with the name Thor not technically being a title, but it is a name that's come to represent something over time and him letting someone else honour his name by doing the things he no longer can makes total sense to me.