I did this in my first characters in Demon’s Souls and Dark Souls 1, when those originally came out, with a character named Brothbarrel. Brothbarrel was a very large and grumpy middle-aged bald man with as close to black-metal corpsepaint as you can get in those games. I think he was born out of being completely incapable of making a non-ugly person with those early Souls character creators, giving up, and just trying to make the grumpiest person possible. He started Demon’s Souls as a barbarian and ended as a knight, so naturally in Dark Souls I started as a knight and ended as a paladin. I liked the idea of him continuing his arc of self-improvement across time and space.
I also used a family-based naming scheme in Dungeons of Dredmor, where every character on every run followed the naming convention of “(Fruit or Vegetable) Quincy,” and I imagined they were all related in some way, each delving into the dungeon to try and find out what happened to the last one who went in. So I had for example Yams Quincy, granddaughter of Broccoli Quincy, who herself was the cousin of Asparagus Quincy, the son of Arugula Quincy, Vampire husband of Apples Quincy, etc. I have no idea why I started doing this but it was a fun challenge to think up new fruits/vegetables I hadn’t used before for each run, and it imbued the game with a sort of tragicomic personality entirely of my own making that I haven’t really experienced in a game before or since. I never did avenge the Quincy family legacy though, because I am shit at Dungeons of Dredmor.
Nowadays I almost always play as female characters whenever possible, since it’s nice to be able to express gender in games in ways I don’t feel comfortable expressing yet in real life. The only through-line is that I often use plant-based names, which I hadn’t realized was sort of a continuation of the Dredmor scheme until now lol.