Initially, Mozilla engineers wanted to call their new open source browser Firebird, but in researching the name they saw another open source project had already grabbed Firebird. In the spirit of open source etiquette, they decided to look for another name. Firefox, another name for a red panda, was chosen for relatively simple reasons.
“It's similar to Firebird,” says Mozilla in a blog post. “It's easy to remember. It sounds good. It's unique. We like it. And we weren't able to find any other project or company even remotely similar to a web browser that uses the same name.”
Mozilla, on the other hand, has more epic origins. It was originally a code name for Netscape Navigator, which combined the words “Mosaic” (an early browser) and “Godzilla” (the movie monster).