I really hate that people focus on the faithful echo for this one and not the diving phoenix, the auspicious phoenix, or the great phoenix.
That's because "鳳" isn't really "phoenix". It's a fiery mythical bird, so it often gets translated as such, but it doesn't resurrect from its ashes like a phoenix does. On the other hand, "不死鳥" is 100% a phoenix, so it makes sense here.
