Is there a word for a person who acts a certain way to become friends with others of a higher or more important social status? Someone who will act falsely to impress others for their own gain (i.e to then show off about it to "lesser" people, in a "look who i'm friends with" style)?
Sycophant — M-W
noun a person who praises powerful people in order to get their approval; a servile self-seeking flatterer
"when her career was riding high, the self-deluded actress often mistook sycophants for true friends"
You could use Pretentious to describe such a person.
having or showing the unpleasant quality of people who want to be regarded as more impressive, successful, or important than they really are
Used in a sentence:
John used to be an alright person, but ever since he started hanging around with Roger he's started acting quite pretentious.