Firebird vs. Mozilla

Traditionally, as I'm sure you know, a trademark is only applicable in a certain domain. 'Using the name first' doesn't grant exclusive control over that word forever, except perhaps if the word is entirely made-up. There are plenty of companies and products which have the same name as each other, and as long as they're not competitors, or in sufficiently similar domains that there might be honest confusion between them, there's no problem.

It seems however that 'things related to computers' is one domain now.

It's silly that two entirely unrelated software products can't have the same name, as if the field of 'software' were similar in breadth to, say, 'washing machines'. I think this is going to have to change as people realise that 'software' isn't all one thing - otherwise we'll run out of words.