Kloster means monastery (cf. cloister). Halfen doesn't mean anything in high German anymore, but it looks related to half (halb in German). I think the name stems from some late medieval tenant of land belonging to a monastery or sth. like that.
(tbh the surname sounds slightly funny for a native speaker).
It is a very surprising move. Apparently there had been rising tensions with her coach of 6 years (who is also a federal coach), maybe also connected with her injury. But nothing of that came into public.
While there are a few decent middle/distance runners in Germany, there is nothing remotely comparable to NOP or Schumacher's group. While some runners are joining larger groups for training camps, there is no group with top level runners, even apart from the fact that there is nobody in her class in Germany. (Alina Reh is very good but mostly on longer distances and slowish below 5k, Krause is a very good steepler but only decent over the flat.)
So to improve her environment Portland was basically the only place she could go.