Name is "Castle Cerwyn"
This was redirected to just "Cerwyn" a while ago.
There is no real systematic reasoning behind this, but some Houses have the same name as their castle-seat, in which case sometimes the name of the residence includes the word "Castle", other times not.
This location is consistently called "Castle Cerwyn". "Hornwood" might not actually be "Castle Hornwood" because that hasn't been used consistently like this.
Reasons for the change back to "Castle Cerwyn" are:
1 - Sansa in episode 6.8 "No One" clearly calls it "Castle Cerwyn".
2 - The HBO Viewer's Guide map has an entry for it titled "Castle Cerwyn".
Which seems proof enough.