Prince William's last name is Mountbatten-Windsor. The royal family, typically, does not need to use a last name. However, this last name is used by direct descendants of Queen Elizabeth II, when they have an occasion to need one, such as upon marriage into the family.
Prince William's given name is William Arthur Philip Louis. He was born on June 21, 1982 to Prince Charles and Princess Diana and received the title "His Royal Highness Prince William of Wales". He has one younger brother, Prince Harry. He married Kate Middleton on April 29, 2011 and they were given the titles "Duke and Duchess of Cambridge." On July 22, 2013, their first child, George Alexander Louis, was born. Prince William is in line to become King of the British Commonwealth after his father.