The only time I remember the character of The Doctor referring to himself as "Dr. Who" was in the Peter Cushing movies.'The Doctor' is his name, I think he's only named himself 'Doctor Who' on one occassion (which was an extremely early episode), so why should the credits read anything other than 'The Doctor'?
It would be like Harry Potters credits reading
Snugglywugglygoggleboy - Daniel Radcliff.
I know that's not entirely the point, but I'm sure people get what I mean.
I only remember the W.O.T.A.N. computer in The War Machines calling him Dr. Who.
Other than that, it's always been posed as a question. First by William Hartnell, in the very first episode of the show, and then by many others since. (Too many IMO. The joke has worn a bit thin)
Am I forgetting any other times that he was actually referred to as "Dr. Who"?