Well first of all let me just say I have a few different characters. Due to an intense case of re-rollitis, if I didn't I would never finish with one character. So.
My Khajiits name is Do'isa. It translates to "ice warrior". My Orsimmers name is Andromeda - this is because the story of Andromeda relates closely to her backstory. I just thought it fit and was a neat name besides.
My Altmers name is Wren Mnemosyne. It essentially translates to "dark memory". Again, it's related to her backstory.
And finally my Bosmers name is Serah Estiph. Her first name translates to lady of song, scent, the morning star; also translates to a weapon or piece of armor in the literal sense. In the Bible, there was a woman named Serah married to Jacob who she lived an adventurous, nomadic life with.
Estiph, if I remember correctly, translates to staff or some such. But mostly it's just her last name or family name.
Have made a few new characters since I posted this, so I'm updating this post.
My Khajiits name is Gypsy Moon. Was originally going to be Gypsy Amaris, which means "traveler child of the moon", but I messed up her appearance and had to do her over again. So, wanting to differentiate the two, I renamed her Gypsy Moon. Just think of it as meaning the same thing.
Then there is my Dunmer, named Ianthe Tinúviel, which translates to "purple nightingale" or "purple night flower". If you can't already tell she's going to be a Vampire Lord.
And finally my Nord, Nymeria. It's a reference to Arya Stark's wolf Nymeria and the warrior queen Nymeria in Game of Thrones. Nymeria will be a werewolf and also have hunting dogs to help her in human form.