OP, I hope I can help.
Bethesda follows what I assume are just a few simple, unwritten conventions to create new Dunmer names. Since you obviously don't know what those conventions are, I suggest you look up a list of Dunmer names that already exist, attempt to deduce these conventions on your own to the best of your ability, deliberate on the subject for a day or so, and craft a few names for yourself. You'll get better at it the more you do it, but the key is patience - don't pick the first name you happen to dream up, because in a day or two you may realize that it's not actually any good.
The same holds true for any of the races, by the way.
Bethesda also uses actual culture for...well, everything; not just names. The Redguards, for instance, are based mostly on Moorish culture, while Nords are obviously Nordic. When it comes to names, I don't know what they use for every race, but there are some obvious ones, like that Imperials are influenced by Roman culture and Bretons by the French.
I understand your desire to come up with something unique (that is, not previously used by Beth) that's also cohesive with the in-game culture. Look for inspiration anywhere you can and match accordingly.
My mage, for instance, is an Altmer named Amadeus, after Wolfgang Amadeus Mozart. I'm a musician and the movie Amadeus (as well as Mozart himself) was very important to me in my youth, and luckily enough, it fits perfectly with Altmer names.
He hasn't been created yet, but I'm going to make a Dunmer vampire named Sorin Markov. Again, I find myself lucky because the inspiration for this name fits perfectly into the Dunmer nomenclature. The name comes directly from Sorin Markov of Magic: The Gathering, mostly inspired by the fact that he's an awesome vampire and that I use a black deck (I'm truly in love with Earth magics, though, but that's another story).
The Orc I plan on creating is probably the best example of changing names to suit TES culture. His name is going to either be Garruk gro Ulamog or Ulamog gro Garruk; I still haven't decided which sounds better. Garruk, after Garruk Wildspeaker and Ulamog after the Eldrazi creature, both from Magic: The Gathering (in case you can't tell, I really love Magic). It's pretty simple to combine the names and it has a very Orcish ring to it.
Altogether, naming your character should be an important decision for you, and as long as you do what I usually do and use an important inspiration, you're going to be very satisfied.
I, in fact, once had a Nord named Isaac Wolf-Heart, named for my love of wolves, their courageous nature and the Triforce of Courage (hence Wolf-Heart), and Isaac from Golden Sun. I was very pleased when, playing as him, I came across a book written by another Nord...the book was titled "Nords of Skyrim," a piece of cultural history, written by a man I'd never heard of before: Hrothmund Wolf-Heart. It was an amazing experience; I had found my ancestor!
I can only hope you have an experience like that. Good luck naming!