Andrew, the scandal-scarred younger brother of King Charles III, will be stripped of his title as prince, an extraordinary punishment — unheard-of in the annals of the modern British royal family — that caps his fall from grace over his ties to the convicted sexual predator Jeffrey Epstein. In a statement on Thursday, Buckingham Palace said it had begun a formal process to remove the “style, titles and honors of Prince Andrew.” The prince, it said, “will now be known as Andrew Mountbatten Windsor,” the family name of members of the House of Windsor. The palace also said that Andrew, 65, would be evicted from his sprawling residence, Royal Lodge, and move to a private house. Andrew has steadfastly denied that he raped the woman, Virginia Roberts Giuffre. But doubts about his account of his relationship with Mr. Epstein — as well as sordid details of his sexual misconduct in a newly published memoir by Ms. Giuffre — made his position in the royal family increasingly untenable.