King's full name was William Lyon Mackenzie King. He was named after his great uncle; William Lyon Mackenzie, Toronto mayor, rebel and republican. You accepted William but put Mackenzie as the answer. His first name was William. His last name was hyphenated as Mackenzie-King.
His last name was King, not Mackenzie-King, and the name he used most was his third given name, Mackenzie, rather than William, his first name, which he never used. We accept either. See the first paragraph of this article.