@VonSupponnatime said:

Might it be a good idea to rename the classic DW series as "Doctor Who (1963)" (or rename the new as "Doctor Who (2005)") to differentiate the two?

They don't do that here on tmdb. The name should just be the original name; no extra info (like the year or a country code).

A quote from a section from the contribution bible:

"There should be no extra info such as the year of release "MacGyver (2016)" or a country code "Shameless (US)" added to the titles."

I guess its possible they might change their minds in the future, but I think atm its a no for adding years on titles to differentiate between series with the same name (and a no in general to adding years on titles). Also, there are already other ways differentiate; things like different posters, backdrops, cast members, trailers, overviews, etc.

Yeah, as @tmdb24407783 pointed out is it against our guidelines. And the year of release is already included in the search: https://www.themoviedb.org/search?query=doctor%20who