Neither Danny Pink nor Clara Oswald liked their surnames, Pink and Oswald respectively. (TV: Listen)
Jocrassa of Raxacoricofallapatorius clarified to the Ninth Doctor that Slitheen was his surname rather than his species. As noted by the Doctor, Raxacoricofallapatorians were distinguished by their use of hyphenated surnames. (TV: World War Three)
Rodrick cited Rose Tyler not knowing the Princess Vossaheen's surname as evidence that she was stupid. (TV: Bad Wolf)
The Mantraps, created by the Dots, ate the residents of both Finetime and the Homeworld in alphabetical order by their surnames. (TV: Dot and Bubble [+]Russell T Davies, Doctor Who series 14 (BBC One and Disney+, 2024).)