Whatever sounds lore appropriate:
Dunmeri: Baltis Llervu, Balthis, Revarn, Llathandes Dramir, Peren Dramir
Nord: Aesrin Stormsong, Eiswulf Stormsong
Breton: Caspar Gray, Galen Alenje
Redguard: Cyrus (), Ralen
Imperial: Aless, Marcus

and more, I just can't remember.

The only two names I would really connect to TES lore out of my four RP characters are the Dunmer knight Endar Telvanni (Has been my main character from Morrowind to present in Skyrim) and the Khajiit thief Ja'Zin-Dar.
My other characters are the Nord named Imsin the Huntress, the Altmer conjurer Skye, and the Imperial storm mage named Arlowe.

I also have RP'd Imsin into a dremora (Made a deal with Hircine to return to Nirn, no longer a werewolf, but "remaining" immortal as a dremora battle-mage) and her name is Iyazyr - the names of two characters of the daedric alphabet.

I'm not much of a nord fan. I did make a khajiit once named Shavaash Opress. Haha. I forgot about him.

I like to stay lore-correct, at least in the broadest sense.

Hridi Oak-Eye, Nord shaman
Shura gro-[censored], Orc mage
Ieneth Hlervu, Dunmer rogue
Do'Renji, Khajiit warrior

In Oblivion, I named my Dunmer character Aelah. I thought that name was fine and kind of appropiate for a Dark Elf. Looks like there's a Nord Companion with this name in Skyrim and she is also a huntress. When I play this girl I wear only light armor or robes and city clothes.

My Skyrim character's name is Athyn. Cuz I just like that name. He's an archer. I also RP'd him in Morrowind. It doesn't mean my Dragonborn is also the Nerevarine. Separate universes, that's it.
Another character I play around with in Skyrim is Kahmet. She's an Altmer archer-mage. I came up with that name and can't tell how.

My Morrowind character and my personal favorite of all this bunch is Theya, a Breton Spellsword and Mystic. I might RP her in Skyrim too, just personality-wise. I'll create another backstory etc etc so that she won't also be the Nerevarine. She favors Medium Armor. My personal favorite is Indoril.

Full names? Here.

Aelah Athrys
Athyn Serano
Theya Liore. I RP her in a thread on these forums. I assure you, she will be just a Temple priest and adventurer in that story. Her name is a spelling variation of Thea/Tia, but it's pronounced differently. It was the name of my dog. D:
Kahmet is just Kahmet.

I have other characters (rogues and mages) that I've never RP'd in a game, but I might because it helps me get to know them better. I accepted the challenge of writing a long, long story and I must know my characters....hopefully I'll succeed at this.

I often name characters of the same race with the same last name, with the idea that tehy are related.

I suppose if we're including the other games:

Daggerfall: Thanelle Cromley, Breton knight (I'd considered Cromwell, but the rhyme sounded silly, and I'd probably be required to try and depose the king or something. )
Morrowind: Ulinth Llanso, Dunmer pilgrim[-ish class] (from Catalan llanca, "lance" - I originally had her using spears, though I've settled more on swords. She was originally "Orthe", but then I ran across a Dremora by that name in Oblivion so it didn't seem to work so well.)
Oblivion: Setentia Merilla, Imperial mage (A variation on Latin sententia, meaning "thought" or "sense".)

And my character in Redguard is named Cyrus, but apparently that's what everyone names theirs.

Morrowind: Hloyrl Antyvar was my Dunmer Nerevarine. He mainly used longswords and a shield.

Oblivion: I made quite a few characters but the only one I kept was Cyrian Kane, a Nord raised by Bretons in the Reach. He was equal parts thief and warrior and used anything really.

Skyrim: My primary character is Trojdan Tree-Breaker, a Nord who specializes in the bow and fire magic (Tree-Breaker is a Norse kenning for fire).

He and the cook in the Underkeep must get along great, then!

I forget my old characters' names, honestly, but my current Redguard is Alusaron Harker, an itinerant bard, auto-didactic scholar, and part-time thief with a generally affable manner, a heart of gold, and a mean pair of scimitars. He is also old and has a beard.

Skyrim:

Sullah-Hakiem: Male. Redguard. Refuses to use magic. Two-Handed / Heavy Armor specialist. Non-confrontational if he can talk his way out of a situation. Obsessed with getting rich.

Driw: Female. High Elf. Sneak / Archer / Mage. Covert Thalmor Operative. Her mission is to destabilize the Imperials by any means. Allied with the Stormcloaks (for now ).

I like to create a lore-relate name, or as close as possible, as well as trying to give them some backstory. My whole experience becomes a lot more fun for it.

I've made quite a few Khajiits in my time, but my main character that I've played through both Morrwind, Oblivion and Skyrim with is Ri'Tenya. ''Ri'' is a Ta'agra prefix that shows status, quite like the prefix ''Ra'', except ''Ri'' denotes a higher status like tribal leader and such.

I've also made an Argonian Shadowscale by the name of Kahjum-Tei, my primary assassin character. His Jel name (language of the Argonians for those who do not know) translates roughly to He-Who-Seals-Fates. However being an Argonian his language translates poorly to the tongue of men, and the actual meaning of it is much more abstract, being closer to He-Who-Resolves-The-Cosmos, or He-Who-Upholds-Order. The Argonians being in touch with the Hist have a different view on life and death and time, and so the birth of the Shadowscales are viewed as a purposeful necessity. (Needs to be mentioned that this is completely fanmade speculation, based on some of things we know.)

I also like fidgeting around with Nords. Being Norwegian gives me the oppurtunity to create very norse-sounding names that also sounds TES-Correct.

Cato [Bombyphorus Tasus Alessia Cheydinius et] Vividus: Cyrodilic Scoundrel. Likes Bows and Light Armor.

Alviss Lotus-Eater: Nord Battlemage. Goes in Gandalf-style: Sword and Staff.

Tauvthanarati: Altmer Barbarianness. Likes big weapons, doesn't really care for armor.

Pantagruel: Breton Mercenary. Sword & Board.

My main is a nord 2h warrior called Penderghast, in both Oblivion and Skyrim, and will be in Morrowind when I get around to backdating. The rest of my characters always have lore-accurate names but I just pick random ones that sound good at the time from UESP.

I usually just use the Tamriel Rebuilt name generator and then just tweak a selection to my liking for the character.

My Nerevarine was a Reachman called Escua, a master of the spear who had a wolf companion called 'B' with a coat as black as night. There are rumours that he left Morrowind on an expedition to Akavir and age ago and has not been heard from since.

My Dovahkiin, Jonethyn, is a Nibenese farm boy that is descended from the ancient but meager House Ysciele in High Rock.

Also have a Dumeri nightblade in Skyrim called Erenir Andrano, going by the moniker Erenir Shadow-Hand. Born after the Red Year and grew up on Solstheim - He is Boethiah's Champion and a true Padomaic, wreaking havoc from the shadows with blade and fire across Tamriel.

Edit: Forgot my COC, Ana. She was an Imperial, the daughter of a high ranking Imperial Legionnaire who fancied herself a hero out of a bard's tale. In reality, she was little more than a sellsword who ended up getting thrown in jail. These days she is known as the 'Sithis-Shaped Hole of the World', AKA Sheogorath.

Ah so he's an unchanged Chimer then? Fascinating.

Nerevoth. I just combined Veloth and Nerevar. He wears Solitude guard's armor because it looks nice on him. Monk like class, I use hand to hand even though it is wildly ineffective.

Arvus Indoril - Male Dunmer, Ex-Morag Tong became Tribunal Patriarch and mage. (main: Nerevarine / Champion of Cyrodiil / Dovahkiin)

Ashiharu Urshilaku - Male Ashlander Dunmer, Morag Tong

Rahjin - Male Khajiit, Thief

Khaj'dro - Male Khajii, Elsweyr Prince exiled to Skyrim and adventurer.

My Dunmer battlemage/werewolf is called Sedri Dreth, and my Argonian warrior/vampire is called Heedal. So I tried to make them match up with other Dunmer and Argonians.

My Imperial is named Scipio Africanus, I always name them that.

Why the last name Africanus? Was his father's first name Australopithecus? Ahurrr hurrr hurr.

Let's just say that he was a robust specimen.

In every game I'll at some point play a female mage called Miyu (always Breton in TESs). For Skyrim I made up some specific lore, though.

For Dro'Darsha I actually looked into a Khajiit dictionary to find a fitting name.

For other characters, I look into uesps race-specific NPC lists to get a feeling for the lore.

1. My Main character is a long haired Nord named "Ehrl". Ehre / arya meaning 'Honourable, Nobleman, Civilised' etc which is Indo-European in origin as in the root of the words Earl, Ehre & Arya(n).
For armor...
Skyrim = Dragonbone armour (minus the helmet)
Oblivion = Crusader armour (from Nights of the Nine)
Morrowind = Nordic mail (from Bloodmoon)


2. My second character is a Khajiit named "Ra'ja" (though in Oblivion I called him "Ra'ja-Hajiit"). I have based him on an Indian Rajput warrior.
Ra'ja is a light armoured swordsmen warrior with blade and shield. He is also an ace with a bow.
For armour I am a bit sticking to thieves guild armour. Its a shame TES don't make a Khajiit armour

In Oblivion I also made a ...
3. Bosmer called "Angkor". elven armor with a red hood and specialised with a bow.
4. Imperial called "Maximus". military haircut and wore Imperial dragon armor (ebony)
5. Orsmer called "Mundzuk" (the name of one of Atilla the Hun's brother). Orcish armour and favoured an axe.

You and I make quite the Paranthropus.

I only have 3
Nord: Sifken the Avalanche
Argonian: Tull
Khajiit: Taela