The Beaufort surname (properly de Beaufort, "from Beaufort") probably reflects the birthplace at the castle and manor of Beaufort ("beautiful stronghold") in Champagne, France.[5][6] The Portcullis heraldic badge of the Beauforts, now the emblem of the House of Commons, is believed to have been based on that of the castle of Beaufort, now demolished. John of Gaunt was married three times. During his second marriage to The Infanta of Castile, he had 4 children by his mistress. Once he married their mother, It took a Papal Bull and an Act of Parliament to legitimize these 4 kids. They took the surname Beaufort but their half-brother, Henry IV kept their names from the line of succession. The eldest became John Beaufort, 1st Earl of Somerset. His son became John Beaufort, the 1st Duke of Somerset. One of his daughters became Joan Stewart, Queen Consort of Scotland. The other three were.
Cardinal Henry Beaufort, Bishop of Winchester (1375–1447)
Thomas Beaufort, Duke of Exeter (1377–1427), married Margaret Neville, daughter of Sir Thomas de Neville of Hornby by an unknown wife
Joan Beaufort (1379–1440); married first Robert Ferrers, 5th Baron Boteler of Wem, and second Ralph Neville, 1st Earl of Westmorland.
Joan's daughter Cecily, Duchess of York, was the mother of Edward IV and Richard III. So, The Beaufort children did alright.