It was Project Phoenix (resurrection of the Netscape browser). This resulted in the Firebird browser (Firebird and Thunderbird). But Firebird was an existing database that objected to the name. So, we got Firefox instead.
All the first 3 names were taken. They probably had to bribe even the holders of the Firefox trademark to get it (though the terms were never disclosed).
Mozilla was sued to rename Firefox (like I said) by one Phoenix Technologies. If I remember right, they picked two bad names before picking "Firefox" but I don't remember the other one.
It was Project Phoenix (resurrection of the Netscape browser). This resulted in the Firebird browser (Firebird and Thunderbird). But Firebird was an existing database that objected to the name. So, we got Firefox instead.
At least that is how I remember it.