I think this is a good way to look at it. I don’t want another character like me. I have MANY characters, and they all have a part of me in them somehow but I like to make them all different and I ain’t looking for me in a book. I want my name. I can relate with characters elsewhere.
I just like to see that Monica’s are included in books, too. So I wanna add one.
But honestly, yes. I didn’t even think about that but even characters without your name can end up being a self-insert so the name doesn’t really hold much weight, other than looking pretty on a page and having meaning to the author in some way.