Song from the Lost Cities because she had ruined the family name by nearly flooding Atlantis, and also because they wanted to be free of the shame of twins so that their family name would not suffer anymore.
The surname "Song" (originally "Tong") comes from many different human Asian cultures-- it can be a Chinese, a Vietnamese, or a Korean surname. The first names of the family members are of Vietnamese origin, but on the other hand, they have been described as looking like "K-pop idols" or "like they'd stepped straight out of anime", so the lines between the different cultures have been blurred, when it comes to the elvin Song family.
In the books, he seemed harsh and rude to his children, but cares deeply about his wife, Mai.
She is shown in Book 5 Lodestar and Book 6 Night fall that she wants to start this over, and asked that she want them (The twins) back to her life.
(Tam Song and Linh Song made it clear that they are twins)