I've never once given a character my birth name, as I'm not fond of it as a first name. (I wouldn't mind it as a middle name, just not my first. and no, my real name isn't Alex)
I've used my 'preferred' name in exactly one pokemon game and that was when I played as myself in Shield.
(I've used it a few times in other non pokemon games as well depending on whether or not I'm playing as myself)
For every other pokemon game I've played, I'd name the protags after different characters from stories I make myself,(Alex being one of these) or something random that I liked.
(some examples of this would be 'Sammy' or 'Zack' from FR, 'Mark' from HG or 'Naomi' from SS and so on)
My most recent protag in Violet is named Nova, after a character in the most recent story I'm working on. (Whose full name is Novellia Delce BTW)