Basically I do not like most of the names in the Tamriel Rebuilt name generator, at least not for my own personal character, they are great for random Dunmer.
Some of the Names I ahve used usually incorporate known Dunmer last names with new Dunmer first names.

Neveril Indobar for instance is one.

Vuhoni Sul Selbar is another.

Come up with some unique Dunmer sounding names.

Avoid Drow names if you can. They are not the same thing, not even close.

I can't recall if any of these names appear in the games, but I made them up myself - they're fairly Dunmer I think.

Devos Uurath (M)
Nera Culrayn (F)
Syran Myl (M)
Bolar Drun (M)
Dengar Herys (M)
Owar Ven (M)
Vunilea Methylon (F)
Moras Oresdar (M)
Fera Feranim (F)
Tervus Safrys (M)

Edit:
Oh, and by the way, what are "Drow" names?

geez i though i was original when i picked orvas as my dunmer spellswords name, i just picked one i could spell on my morrowind playthrough, and used it for my next character

Nice they feel pretty Dunmer-like.

Drow are the Dark elven race of the Forbidden Realms series. basically D&D. They have names like Zaknofein, Drizzt Do'Urden, Jarlaxle Baenre, etc etc.

Nineveh Anyrmd
Anydro Naramsina
Domara Barsuun

Here's a few of my attempts:

Okaryon Hlervu

Merylsek Adur-Dan

Dulzleru Dreloth

Seeth Chodala

Hokarees Telvayn

Jeluu Zeba-Adad

Uldray Omaren

Usem Yentimilal

Vohq Dareleth

Rhesn Kutebani

Sundris Madura

The dunmer name I tend to use is

Azarel Llendos

Daren Neldros
Saryn Andaras
Ules Tarandos
Silvas Ulvireth
Redas Vlales
Andar Resdath
Nelos Tarcaryn
Ferath Lys
Riesan Undalas

Vynith Uulandas
Viryn Hlaalu
Delos Llandus
Telvyn Dulveyn
Neloth Ulen
Jiub Jiubson. :3

Vedaa Addammassar

That's the name of the Dunmer I use.

The name I use for my Dunmer is Temujiin. And I guess I'd use something like Hlaalu, though I've not used one.

Temujiin is the real name for Genghis Khan (Genghis Khan just means 'great king' or something similar).

Temujiin's family are from Dunmer Ashlanders

That's cool. My character is also from an ashlandic family. What is your clan's name?