I meant only one character, the one I'm controlling. Like in Dragon's Dogma. :)

In party games, then, how do you name the rest of your party?

And what if the game decides to reject your name, or if the game doesn't provide enough space for your name? (Some older JRPGs only allow 4 character names, for example.)

For the rest of the party, I name them differently. I don't play rpg games much but the ones I've played allowed me enough space for my name.

Isn't it obvious? Arsalan1, Arsalan2, ..., Arsalan12. :-D
I heard that Arsalan7 died in a damp ogre cave. Sad story...

I've once in a great while named characters after friends and family... but never myself.

I usually use my gamer tag "SkeletonBow" in most games, however when it is an RPG and you get to name your character, I usually create a custom name for them. I make up names that are fabricated by a combination of real world names (modern or archaic), either combining 2 names together in some way, like "Elizabeth" + "Gwen" = Gwenabeth, or by taking part or all of a name and adding a medieval sounding ending to it. Sometimes I just make up a bunch of letters that sound cool together and add a typical medieval sounding ending to it.

Just making some up here for examples:
Barthovere
Elwyndoth
Morphelus
Georganthar
Jeremyral
Hrothgantel
Jessantha
Danielistryde

When in doubt, all heroes get cat names so that all games can be about cats even if you don't see cats in the game.

Just for fun, I decided to ask Mistral OpenOrca 7b to come up with some RPG names that sound medieval and unique and here is what it came up with:

1. Elerian
2. Narissel
3. Rodryn
4. Tharvyn
5. Seldris
6. Jylariel
7. Eldrylle
8. Keldraneth
9. Malvarin
10. Edrelyn