On-screen,the Time Lord was only clearly referred to as “Doctor Who” in one story ("The War Machines").
However, prior to the start of Peter Davison's tenure, 'both Dr. Who' / 'Doctor Who' were officially accepted ways to refer to the character - in the the programme's credits, the listings, the official BBC production paperwork, etc. etc.
And contrary to what many would have us believe, during the 'classic era' it was also a quite acceptable and commonplace convention - for fans, the British Press, and public alike - to refer to the Doctor as: 'Dr. Who' or 'Doctor Who'.
As evidence of this, each of these clippings make some reference (however slight) to the Time Lord himself as: 'Dr. Who.' / 'Doctor Who'