Shin Megami Tensei games have you rename their protagonist (and often the 3 other central characters too), but most of them don’t have a canonical name. Also most of the time those people are supposed to be Japanese. Every time I am starting a game like that I struggle to choose a name that doesn’t stick out like a sore thumb for them.

If there is a default name, I usually use it. Exceptions are the kind of RPG where the character is a blank slate, whose identity doesn’t matter at all and whose appearance is custom (like Elder Scrolls, Fallout, Xenoblade X for example). And stuff like Pokémon, obviously. When your avatar is going to meet other players, doesn’t look good if everyone has the same name.

I started Xenoblade Chronicles X (Wii U) without even knowing the main character had a canon name (it’s… Cross. Like the X is supposed to be pronounced in the games’s title). But even if know it now I still rename them. They are custom, there is multiplayer, and story-wise they’re the blandest of characters anyway, so…