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1.
False fame. The false sense of notoriety and ego inflating self fellatio achieved by self published authors, terrorists, tweens with massive friend lists on social networking sites, and dipshits being milked for lulz. Basically anyone who flaunts their "fame" but doesn't have any money to show for it.
Jonathan Robin spent a small fortune over the last decade buying points at allpoetry.com so he could advertise his work to other shitty poets. That guy is fucking faimous!
by Matthew Kastor May 15, 2013
 
2.
An abbreviation for the Facebook Chat application. as in Facebook-AIM so in turn; FAIM
"Hey, I'll catch you later tonight on FAIM!"
by Arpen Jhaveri February 12, 2009
 
3.
Facebook AIM. A service referred to as Facebook chat that enables one to communicate with fellow Facebook buddies.
Judy: Hey I was talking to Brad last night on FAIM, and he told me I was hot.
Lola: He's probably lying. Guys always lie on FAIM.
by bweezy11 October 28, 2008