Dull old soul that I am, I take a literal approach to these things. Both of the two characters I've played have been Bretons, so I used t'internet to look up actual real-world Breton names. (I know Bretons from High Rock are not the same people as Bretons from northwest France, but...shut up. I'm doing my best.) A spot of googling rapidly found me a list of known Breton names from the mediaeval period, which seemed just about right; then it's just a matter of choosing. I expect you could do the same for Nords to find lists of Scandinavian or Germanic names, and I'm absolutely certain you could do it for Imperials with Roman names. Cats, elves, and scalies, not so much.
I have never played a Khajiit or an Argonian character. I would probably name the Khajiit: Meows When Wet or Licks Own Fur. For the Argonian: Tough-As-Shoe-Leather or Basks-In-Dragonfire.
Most of my characters have names like Fus Do Magoo, Super Douche, Turdly Fergusen, or my current Shadow Swordsman (inspired by Henson's Hashashin) character is named Slasher McSplatter. I don't see much in a name since your character never talks and never introduces him/herself to any NPC. I love to RP my characters, but names mean nothing to me for a personality in my own mind anyway. Might as well make myself laugh when I see the name in the skills menu.
I named my Argonian Lizzy ...I know real original LOL. I had another Argonian I named Zatara.
Other characters: Orc- Malaki, Dunmer Vampire Elisse, Arielle was a High Elf, Morwen and Kelwen were Wood Elves, Ripley was a Khajiit (Manticore build), Morgana was a frost knight, Maladrae was a dark elf. Anyway, just some examples of names I have used.
I have never had lore friendly names and my characters just have some random names.
For an example my Altmer mage is called Gandalf. (I am the most original person ever.
My Orc warrior was named Gug The Crusher. (Accidently deleted save file. R.I.P. Gug.)
And my Bosmer archers name is Little Elf. (Just because.)