You're right. From here :

http://www-archive.mozilla.org/projects/firefox/firefox-name-faq.html

It was Phoenix from 0.1 to 0.5 however Phoenix bios already had Phoenix name.

It was Firebird for 0.6, 0.6.1, 0.7, 0.7.1 (for Mac) however the open source Firebird sql had Firebird name first.

Firefox started at version 0.8 and continues to be the name since.