Monkey Builder seems popular but it doesn’t really work as a name for me. It is what it is but it shouldn’t be what it’s called.
It’s almost like if people started calling me Human… well yes I am a human, but that’s not my name. Unless of course I get abducted by a superior alien race…
Human… bring me my goblubular you wretched inferior beast.
SpaceShift Editor worked because it was unique, whenever it was mentioned I knew what people were talking about. However Monkey Builder could be anything.
There are some precedents set here though; SpiderMonkey, Lemur et. al. Maybe you should consider another unique-ish name.