The last time I was there (about three years ago), the station signs said just "Cark".
It seems to change roughly as often as the TOC changes its socks (or station nameboards, at least). The on board announcements on Class 185s definitely say "Cark & Cartmel".
It probably makes sense to drop the suffix completely, because if going to Cartmel you're better off getting off at Grange where you might have a hope[1] of a taxi or (during the day) bus connection.
OK, if you're walking the walk from Cark is a bit nicer (done it myself), but who on earth would be walking that (a short hike, really, requiring appropriate clothing and a torch at night) who hadn't already looked at a map to decide which station to use?
[1] No guarantee - the taxis are mostly one man bands and you have to ring round, and if they're booked, they're booked - there is no big taxi firm operating any nearer than perhaps Ulverston or Barrow.