In season 1 episode 7, "You Win or You Die", of Game of Thrones, the scene where Ned tried to expose that Joffrey is Jamie's bastard, not trueborn of Robert, Joffrey is shown to be styled by the names of both houses, Baratheon and Lannister:
All hail his Grace, Joffrey of Houses Baratheon and Lannister, the first of his name, King of the Andals and the First Men, Lord of the Seven Kingdoms and Protector of the Realm.
Is it common for kings to be styled with their mother's house? Because to me, if it is not common practice, then this is not the correct time to do so. Especially when someone is trying to reveal that he is indeed a Lannister bastard and also it implies that the Lannisters are trying to capture the throne.