Casterly Rock is the seat of House Lannister, although there is another smaller cadet branch of Lannisters that live at Lannisport, which is nearby. The Kingsguard are also known as ‘Whitecloaks’. Obsidian is also known as ‘Dragonglass’.
While it’s Martin and Willem in the show. It’s Willem Lannister and Tion Frey who are held hostage in the books. ‘Martyn’ was captured earlier, but was later released in exchange for Robett Glover.