Idiom
give someone a reputation (for doing something)
Theme: REPUTATION
to cause someone to be known for doing something.Her excellent parties gave Jane a reputation for entertaining well.You had better be careful or your behavior will give you a reputation.
Idiom
give someone a reputation (as a something)
Theme: REPUTATION
to cause someone to be known for being something.That evening gave him a reputation as a flirt.Yes, it gave him a reputation.