Great Comment on the Doctor's Proper Name

An anonymous commenter made a great comment on my post '12 Reasons he really is called Doctor Who:'

The other silly thing is that just because he is often referred to as "the Doctor" doesn't mean that his name isn't 'Doctor Who'.

Take the Brigadier. His name is Lethbridge-Stewart. He is referred to as Brigadier-Lethbridge-Stewart and also as just "The Brigadier". However, while the Doctor, Jo, Benton, Yates, Sarah etc. call him "The Brigadier", that is NOT his name. That is what he is. His name is Lethbridge-Stewart.

Likewise, 'The Doctor' is equivalent to 'The Brigadier', and 'Doctor Who' is equivalent to 'Brigadier Lethbridge-Stewart'.