When used as a noun (meaning an adult), is "grownup", "grown up", or "grown-up" more appropriate?
Grown-up is the proper noun and adjective form.
Grown up is the past participle of to grow up.
Grownup is a frequently used form, but more dictionaries prefer grown-up. In fact, if you google grownup definition it returns a definition for grown-up.
"Grown up" is something someone has done. It expresses who or what someone is to a rather minimal extent. Now we are left with "grownup" and "grown-up." So now we have to wonder, appropriate for what? "Grown-up" has a certain childish ring to it, you might use it if you are writing from the perspective of a child or childish person. If you are trying to be informal but not immature, "grownup" would probably be best. I personally do not recommend using any form of "grownup" if you are trying to sound like one, or if you are trying to be formal, go for "adult" or another word instead.