What is Prince Charles' last name?

The Royal Family rarely uses last names, as their titles serve as their names. In the case of Prince Charles, his official title is "Prince of Wales." When he needs a surname, such as in the instance of marriage, he uses Mountbatten-Windsor. His last name can also be considered to be Wales.

Saxe-Coburg-Gotha was the name of the Royal House during the reigns of Queen Victoria and her son King Edward VII, and briefly, during the reign of George V. However, with the outbreak of World War I, a German name was deemed unacceptable for the Royal House, and King George V, on the advice of Prime Minister Hubert Asquith and the Privy Council, issued Letters Patent changing the lineage to the House of Windsor. The present Queen, Elizabeth II still reigns over the Royal House of Windsor today, but as an acknowledgement of the role her Consort Prince Philip plays in the life of the 16 countries of which she is Sovereign, and the 54 Commonwealth nations, and mindful of the fact that for a man the role of Consort is not an easy one, she announced in the 1960s that henceforth she, her husband, and their direct descendants (including Prince Charles, obviously) would use the name Mountbatten-Windsor (Philip's family name) whenever it was necessary to use a surname. It is important to note that this is a private arrangement which does not apply to the wider Royal family (eg. the Kents, the Gloucesters) but solely to her and Philip's direct descendants.