Finstagram refers to the creation of Fake Instagram accounts to post content one would not post under one's real name.
Urban Dictionary defines Finstagram as: "Finstagram, finsta for short, is a mixture of Fake & Instagram. People, usually girls, get a second Instagram account along with their real instagrams, rinstagrams, to post any pictures of videos they desire. The photos or videos posted are usually funny or embarrassing. Only your closest friends follow this account"