I notice when the program crashes, the message refers to it as mscore (likely based on the title of 'Unix Executable File' in the MacOS folder when viewing package contents?).
More than 2 years ago, I talked it over with Werner at FOSDEM in Brussels and there wasn't an easy solution for the binary name. It's a bit of a legacy thing. So I skipped to change the binary name and concentrated to get a consistent naming for all the rest. See http://musescore-developer.685061.n2.nabble.com/Correct-naming-convention-MuseScore-td4560010.html Still I would prefer to have the same name everywhere. So why not look at it again. Perhaps for MuseScore 2.0.