I always use names from mythologies. Minos, Atreus, Nestor, Thesus etc. but when I played sisterly lust I changed all the family names to Mario, Wario, Luigi and Waluigi
I never was able to self-insert into these games. They are always just a story I am reading, but can sometimes influence. I remember when I first started playing renpy games, it would say "What is your name". I would type it in, then it would use my name and I would get really weirded out by it. Now, if I have to choose, I usually use something like Dick or if the MC looks like your typical whiny bitch, I will name them Cuckbitch or something. My way of venting my annoyance at shitty MCs. These days, most devs are good at giving you a default, so I just hit enter and keep what it uses.
I use one of two sets of names (for male MCs and female MCs) depending on how nice/mean or good/evil pure/corruptive etc. I intend to be in the playthrough. When it's not that sort of game I take a guess at what I expect and choose the name accordingly.
I would love to never have to name any character whatsoever ever again. I mean, come on, I'm here to do one thing only, there is no need to get personal or involved. Just like kissing hookers, you just don't do it. Yes, there are some rare cases where the story is really good and a actual gameplay happens, not just a sequence of images and "videos", and it pays to involve yourself a little bit, but, 95% of the time, just go in, do the deed, go out. In the case I have to name them, it's always body parts (Mr. Dick, Mrs Tits, and such).
I never could use my name even in regular games. It was just a constant flow of I wouldn't say that or I wouldn't do that. These days I usually take the 1st letter of the default name and improve it to a cooler one.