Indeed. Originally it was "GAIM" (due to the original purpose being a GTK+ AOL Instant Messenger client), which AOL wasn't thrilled about. We changed it to "Gaim", which I think they had less of a problem with, or at least we had hoped they would.
Internally at least, we called it "Gaim's An Instant Messenger". I'm not sure if we formalized that or not. It's been too long.
And then to fully move away from that branding situation, it was renamed to Pidgin. This was mid-2000s, after I moved away from the project, so I don't have any insight into the name change beyond the history.
As my fuzzier-with-every-passing-year memory recalls, there were a wide variety of interpretations of what "GAIM" meant, with "GTK+ AOL Instant Messenger" being the least offensive one. Mark Spencer, the original author, was always a bit cagey about it--amusingly so to my mind!
I also used the similarly named but jabber only Gajim.
Good times :)