Also of note: Kirk, Spock, and McCoy consistently refer to him as "Mister Cochrane" (as opposed to "Doctor Cochrane" or "My Liege"). It seems odd to me that such a revolutionary scientist in the 21st century neglected to get a Ph.D.
Of course, First Contact tells us he was a Doctor all along. Kirk, Spock, and McCoy were just being rude.
Did they continue calling him "Mister Cochrane" after they discovered his first name?