Officially, there is no such thing as a Point-to-Point Trainer (the term usually applies to licensed trainers under Rules), although many people do prepare horses for Point-to-Points on behalf of the Owner(s). These stables are livery yards, but the people responsible for the horses are usually referred to as Keepers, with their name also appearing in racecards.
Anyone interested in training Point-to-Pointers can find out more from the British Horseracing Authority.