Clapham, Finsbury Park and Croydon are all well known London suburbs, whereas Old Oak Common means nothing to the vast number of Londoners though...
I think the main point with Finsbury Park and Croydon is that you would be getting off there to go to Finsbury Park or Croydon. If you got off there for London you'd have a long walk, and even if you are changing, say from a Victoria to a Thameslink service or vice versa, then you'd probably only be halfway there. Whether the suburb is heard of or not isn't strictly relevant, and I'm not sure many people who don't live in/know people in London actually would know that Finsbury Park or Croydon are London Suburbs anyway.
For most HS2 services into Old Oak Common you would be almost in London, it's the place where half the customers are going to get off and start thinking about onward connections, so there's a better case for calling it London Interchange or something like that. On the other hand it won't be "London" for Crossrail or even GWR passengers. I think you either call it London Western Interchange, so the emphasis is on it not being central and being there for interchange, or you call it Old Oak Common so that people have to recognise and think about it. "London Old Oak Common" just makes it sound like another London Terminus where you can sensibly get off and walk/taxi/cycle/bus to anywhere in the centre.
Not entirely unrelated: Warsaw Wschodnia (East) Station, which is the interchange station not-that-near central Warsaw has just been renamed after Roman Dmowski, which certainly fits the current government's agenda of celebrating slightly dodgy figures from the past, but doesn't really help with journey planning. Luckily it looks like it's just a plaque exercise rather than something that will appear in timetables or on signs.
