Despair's Last Resort: Chiyo Ueda, Arata Miyazaki, and Kazumi Katsuya all do this. Chiyo does it out of politeness, while the other two out of rudeness. Chiyo makes an exception for her Childhood Friend Kumiko. After Shizuka's death, Kazumi refers to her by first name. Arata calls Takara by her first name after she figures out his crime, but it doesn't last long since he gets executed.
In the Gensokyo 20XX series, we have this to somewhat the case with Mokou who is nicknamed "Huzi", being that her last name, Fujiwara, is alternatively pronounced and spelled Huziwara, leading for her nickname to be Huzi and she is usually referred to as such. Apparently, an age-regressed Reimu thinks her first name is her last name.
At least one Mass Effect fic justifies Commander Shepard only being called by their rank or last name by explaining that no one (Shepard included) actually knows their first name.
This Bites!: Partially due to having a different naming convention, all of the Straw Hats call Cross by his last name instead of Jeremiah. This is also on account of Cross much preferring to be referred to as his last name instead of Jeremiah, or any variation thereof.
Chrysalis Visits The Hague: The lawyer Alexander Estermann keeps this going, much to the point that the narration sticks to just referring to him as Estermann, reflecting his somewhat stuck-up professionalistic nature.
Rei tells Kaworu to call her by her last name in chapter 11 of Advice and Trustsince she lost all her memories of him after dying in the battle against the 16th angel (her latest memory backup having been just before meeting him).