Yes, especially the first Firefox logo has a distinct snout. I have no primary source to quote, but there are plenty claims, referencing each other, that the name stems from the nickname of the red panda.
I was wondering if there is any official statement about the name.
But it seems most common to think of a (speedy?) fox with a flaming tail. How to derive a dog's burning relative from a phoenix seems to remain uncertain.
1: https://en.wikipedia.org/wiki/Whataboutism