You know what’s a strange word?
It’s almost exclusively used around kids. You never hear adults referring to each other as grown-ups.
According to Grammar-girl (one of my favorite resources for strange grammar questions), ‘Grow up’ is a phrasal verb and ‘Grown up’ is the past participle* When it’s used as a noun, it needs a hyphen.
*fun fact: present and past participles confused the heck out of me when I learned about them in Spanish class because I didn’t remember ever learning about them in English class first.