According to Wikipedia, Scooby-Doo's name comes from Frank Sinatra's scat line from the song Strangers in the Night. The song was released in 1966 and the first Scooby-Doo cartoon was released in 1969.
However, Sinatra's line is "doo-be-doo-be-doo" and has no "scoo" part as far as I can hear. I wonder where this came from. The 1968 song Picture Book by The Kinks has a line "a-scooby-dooby-doo" which is much closer to Scooby-Doo's name (and practically identical to his catchphrase "scooby-dooby-doo").
Was Scooby-Doo's name inspired more directly by somebody other than Sinatra? Perhaps The Kinks?