Here you go, Maeve:
Fenghuang, commonly referred to as the Chinese phoenix.
Firebird (Russian folklore), an equivalent of phoenix in Russian mythology.
Bennu, an Egyptian correspondence to the phoenix.
Angha, a Huma, Simurgh, Persian phoenixes.
Adarna, a Philippine version of the phoenix.
Avalerion, an Indian magic bird that drowns itself once it has laid its eggs.
Turul, a mythical bird of the Magyars.
Garuda, mythical bird of ancient India.

Heliopolis is the city where the Phoenix hid its egg - that has a nice ring to it. Although, I prefer Firebird. A kind of "in your face" slap at the fire.
Mary