I was speaking with a Russian colleague during a break the other day. There has been the possibility for residents in the local areas of the airports to propose and vote on names for the airports. Many of the smaller regional airports (not on this list) have ended up with names of people only really known in that region.
It seems Sheremetyevo has become A S Pushkin Sheremetyevo International Airport (Международный аэропорт Шереметьево имени А. С. Пушкина) so I am not sure the original names will go away. For now at least.
Tegel Airport in Berlin is named Otto Lilienthal, though no one ever uses that name. Might end up the same way here.