Alexander is from the Greek, alexo (to defend or to help) and ander (or andros), for man. Thus the name means, defender of mankind or helper of mankind.
Mei is a variant of a family name of Jade's: May. On his mother's side, many of the women in his family have this middle name. We chose to spell it as Mei because of its Chinese (and Japanese) meaning: beautiful. It can also mean plum, depending on its spelling. In Hawaiian and Dutch, it is a common spelling for May.
Mei is also a very cute child in the delightful film Totoro.
So where does the name Sasha come from?
Well, we had to make her life difficult, didn't we? Sasha is a diminutive nickname from Alexandra in Russian and many Slavic languages.