To better illustrate, I've setup a Breton character named "Dovahkiin" as the most canon character for Skyrim. Why? Breton's have Dragonskin which ties along with being dragonborn. It was a hard decision between that and a Nord, but I figured since you're suppose to be visiting Skyrim, it would make the most sense.
Oblivion would ideally have an Imperial named "Bendu Olo" since it's (from what I understand) already programmed as default for the character. I've setup Morrowind with a High Elf named "Nerevarine" since I couldn't find any other information about a default name for the main character there. I also haven't played Morrowind past the first quest, so I'm unsure of the full story behind the game (i.e. if there was a better name to suit the character).
I also haven't played Arena or Daggerfall so I couldn't speculate on what the character should be named.
Yes, I understand these games are open-ended as far as what you want your character to be / to be named, but to better illustrate an actual canon gameplay, how would (in your opinion) this be ideally set-up?