The name Mandalore goes to the leader of the Mandalorians and is passed down to the next leader. So its a title more than a name. So, that would mean technically, that Boba Fett would be Mandalore since he is the last of the Mandalorians.
Sure he is. Jango was a Mandalorian and he taught Boba everything about being a Mandalorian and so Boba had all the training that a Mandalorian needed and he inherited the armor, whose to say Boba isn't a Mandalorian?
Nope, Jango wasn't Mandalorian either. He was trained by some of them, but the Mandalorian warrior caste was decimated by the Jedi, more than a decade before the Clone wars.
Interestingly enough; what happened to them is part of the reason Dooku -initially- walked away from the Jedi.
"Creasy's art is Death... and he's about to paint his masterpiece." Rayburn