They couldn't decide between naming him after George Washington or Douglas McArthur, so they compromised and named him McGeorge since Dougshington was just too weird.
McGeorge is certainly more familiar as a surname (The McGeorges are a branch of the MacFheorais family which moved from Ireland to Galloway, in southwestern Scotland).
But I looked up why his parents named him that. From Google:
"McGeorge Bundy was named "McGeorge" after his paternal grandfather, whose first name was McGeorge, as confirmed in biographical documents.
His father was Harvey Hollister Bundy, a prominent Boston lawyer and statesman, and his mother was Katherine Lawrence Putnam.
It's interesting since I think a lot of discussion on presidents boils down to specific things like JFK's assassination, or Nixon's Watergate. Or at least that's how it generally seems.
There are a lot of last names popping up as first names, often as the mother's maiden name. A common mistake is "John Hopkins"... the hospital and university...which is actually "Johns Hopkins."
NB: It used to be obligatory not to omit the "the" from "the Johns Hopkins University." I always thought they were trying to give a Sharper Image patina to their college. They don't seem to be as strict about that nowadays.