bad hat vs troublemaker

bad hat and troublemaker both are nouns.

Word	Noun	Adjective	Verb	Adverb
bad hat	Yes	No	No	No
troublemaker	Yes	No	No	No

As nouns, bad hat and troublemaker are synonyms defined as:

Other synonyms of bad hat include mischief-maker, trouble maker, troubler.

bad hat (noun)	troublemaker (noun)
someone who deliberately stirs up trouble	someone who deliberately stirs up trouble