Unless the name Firebird is dropped, you can't have any animal other
than a "fire bird", whatever that may be.

The image of a Phoenix looks and feels very old-fashioned to me. And
anyway, it carries a rather boring political and inward-looking
message. How about forgetting the idea of phoenix, and
letting "fire" simply mean brilliant red?

I can imagine a cheeky looking head and shoulders of a bright red
bird (like a parrot?) with a broad beak, and mischievous,
conspiratorial eyes, looking straight at us, inviting us to join in
the fun. I can imagine it, but I can't draw it.