Well, the browser that became Netscape was always called Mozilla IIRC. –Brett Morgan's Insanity Weblog Zilla

Jamie Zawinski tells his version of the story of where the name Mozilla came from, in his scary journal of how Netscape 1.0 came about.

A week or two ago we all sat around and tried to think up a name for the client; we can't call it Mosaic, because that's the name of the company. The marketroids had all kinds of silly suggestions like Cyber this and Power that and blah-blah Ware. Then someone said something about crushing NCSA Mosaic, and I blurted out “Mozilla!” Everyone seemed to like that, so I think that might end up being the official name of the browser.

The readme files for each version of Netscape Navigator and Communicator ended with the line: ‘And remember, it's spelled N-e-t-s-c-a-p-e, but it's pronounced “Mozilla.”’