The rename happened over a trademark for another product called phoenix (a database if I recall correctly).
They first renamed it from Phoenix to Firebird due to a trademark dispute with Phoenix the BIOS company (which doesn't exist any more). They then promptly got called out by Firebird the Open Source database project and eventually had to change their name again to Firefox.
Yea, you'd think if you're forced to change the name of your product due to the name clashing with and existing software project/company, you'd take some time to make sure the new name you chose doesn't also clash with an existing software project/company.
They first renamed it from Phoenix to Firebird due to a trademark dispute with Phoenix the BIOS company (which doesn't exist any more). They then promptly got called out by Firebird the Open Source database project and eventually had to change their name again to Firefox.