Cunningham is the name of an old district of Ayrshire in the south of Scotland where the surname presumably comes from.
I wouldn't blame you if you had thought it was English though, people don't always realise the diversity of language heritage in Scotland and think its all Gaelic. The south was actually under Brittonic influence so there's many -ham's.
** You don't have to burn books to destroy a culture. Just get people to stop reading them **