I believe it was originally called Phoenix. Though you're right it was then called Firebird and renamed again to Firefox afterwards.
I think each time was due to trademark disputes?
Going to your point though, I hope you're right but I'm a bit more sceptical. Chromium, being open source, means anyone who doesn't like the stagnation of Chrome would just fork Blink and create their own modern browser while still enforcing the Chrome mono-culture.
I'd love to see Gecko take off in the same way kHTML, webkit and blink have done. In fact I'm surprised it hasn't. I don't suppose anyone more familiarity with the code base of these rendering engines are able to offer possible reasons why?
Not familiar with the code base of the engines, but one factor that distinguishes Gecko vs. the other engines is that Mozilla killed the ability to embed Gecko in other applications in 2011. Read about the detailed reasoning in this mailing list thread. [1] This effectively tied Gecko solely to Firefox, and has made using it with other applications or browser chrome (lowercase, not Chrome the browser) impossible (AFAIK). So it cannot take off like the other engines unless Mozilla puts in work to allow that to happen.
[1]: https://groups.google.com/forum/m/#!topic/mozilla.dev.embedd...
I could see a similar approach working again. Mozilla could focus on user-centric features, while Chrome has to also serve the needs of Google's business interests.