The official names are Rutian and Lethan. The others are known as Ryloth Twi'lek.

But in fanon (information made by the fans for the fans) a woman created a deeper background look on Twi'lek Society including history, ceremonies, religion, culture, customs, a database of first and last names and new race names for roleplayers, writers and the huge twi'lek fans really.

Race Names from the fanon are Torrian, Tyrian, Tukian, Tolian and Darian.

The female Tolian is Ayy Vida (Episode 2 - Attack of the Clones) - she's a nightclub dancer and girlfriend of gangster
The female Rutian is Aayla Secura (Prequel Trilogy & comics) - she was a warrior, a jedi (good)
The female Tyrian is Rachi Sitra - She's a Jedi Knight
The female Tukian is Oola (Episode 6 - Return of the Jedi) - She's an infamous dancer of her village who was seduced and tricked by a man she fell in love with and became a slave dancer/sex slave for Jabba the Hutt.
The female Lethan is Darth Talon (Legacy comics) - She's a trained Sith Assassin (evil)
The male Darian is Nawara Ven (X-Wing Rogue Squadron books) - He's a retired pilot due to a leg injury and a lawyer
The female Torrian is Lyn Me (Episode 6 - Return of the Jedi) - She was offered as a gift to a infamous Bounty Hunter who saved her village but he rejected her. She became a back-up dancer and singer for a rock band who regulary visited Jabba's Palace.

There's one downfall about blue on a Twi'lek, the turquoise ones more often than not have a twin sister or brother. It was said once in a book that Twins were born with blue skin.