Jango was a self-proclaimed Mandalore. There hadn't been one for centuries and, as TCW showed, the Mandalorian people changed. Also, you don't need to be born into a Mandalorian clan to become a Mandalorian. You can learn and be adopted into their traditions and Become a Mandalorian.
Hm? Isn't it, that if the Mandalore dies the first one who gets to the body is the new Mandalore? Cause Jaster Mereel was Mandalore(Jango's adopted father) and Jango was there when he was dying thus claiming the Mandalore title. Lol you know what, thinking about that...that is sort of a stupid rule. XD
Edit: Wait nvrm, Jaster had actual chosen Jango to be his successor before his death. Hmm...shouldn't there be a rule to playing faves? I mean just because the guy is your adopted son, doesn't mean he should have played faves.