reputation vs black eye

reputation and black eye both are nouns.

Word	Noun	Adjective	Verb	Adverb
reputation	Yes	No	No	No
black eye	Yes	No	No	No

As nouns, black eye is a hyponym of reputation; that is, black eye is a word with a more specific, narrower meaning than reputation:

Other hyponyms of reputation include stock, character, name, fame.

reputation (noun)	black eye (noun)
the general estimation that the public has for a person	an unfortunate happening that hinders or impedes; something that is thwarting or frustrating
the state of being held in high esteem and honor	a swollen bruise caused by a blow to the eye
notoriety for some particular characteristic	a bad reputation