Desmond Miles's surname in the Assassin's Creed series is Miles. He is the modern-day character who experiences the memories of historical Assassins through the Animus.
Desmond first appears in the 2007 Assassin's Creed game as a bartender abducted by Abstergo Industries. Abstergo uses him because his ancestry connects him to Altaïr Ibn-La'Ahad and other members of the Assassin lineage. His modern-day storyline continues across several early mainline games.
The surname helps distinguish Desmond from the historical characters whose memories he relives. Ezio Auditore, Edward Kenway, and the Frye twins are separate protagonists from different historical periods, not alternative names for Desmond.
Desmond's role is especially important in the first five main games, where his experiences connect the historical campaigns and the larger conflict involving Abstergo, the Assassins, and the First Civilization. His modern-day perspective also provides the series' recurring science-fiction framework.