"Tenzin" is not a Burmese name. It is Tibetan, meaning "Holder (dzin) of the Teachings (ten)." It's an extremely common Tibetan name since the mid-late 20th century, inspired by the fact that HH the Fourteenth Dalai Lama's name is Tenzin Gyatso. It is, of course, possible that a Burmese-American could be named Tenzin... but the show makes a rather big deal out of Tenzin's Burmese heritage; that being the case, one might reasonably expect him to have a Burmese name.