It does... but it's far less prominent now. The trains don't have it
written on them any more and announcements etc. don't mention it.
Besides which, once the Thameslink work is all finished, the thameslink
route could mean trains to any number of destinations rather then the
fairly simple route it refers to at the moment.

All of which will pass through Farringdon, though. And vice versa, every
train which passes through Farringdon will be on the Thameslink route.

Makes no difference, the name "Thameslink" refers to Brighton / Sutton to
Bedford. Trains going to Peterborough have never been called Thameslink or
part of the Thameslink route, so still calling it Thameslink will be
confusing, especially since the operator won't be called Thameslink either.
Pasting over that sign was a very sensible thing to do.

Best Wishes,
LEWIS