In all the years of classic Doctor Who I hardly ever heard anyone say "Doctor Who", but in New Who people just can't stop saying it.

"Who's he?"
"The Doctor."
"Doctor Who?"

It's quite annoying, actually. We know what the programme is called, thank you, and repetition isn't making it funnier.

It was said a few times in the Classic Series.

The first instance was in unearthly when Ian called him Doctor Freeman and the response "Who?" There are many other examples through the classic years.

It was still rare compared to now. Those clips from classic Who cover 26 years; it's not far off that many in The Snowmen alone!