After Jim Hopper adopts Eleven, she takes the surname Hopper.
Eleven’s birth name is Jane Ives, the daughter of Terry Ives. She was taken from her mother and raised as a test subject at Hawkins National Laboratory, where she was identified by the number 011. After escaping the laboratory, she gradually forms a family bond with Jim Hopper, Hawkins’ police chief.
Hopper initially hides Eleven in a secluded cabin during season two to protect her from government agents and the dangers surrounding Hawkins. Their relationship develops from reluctant guardianship into a genuine father-daughter connection. At the end of that season, Hopper formally adopts her, giving her the legal name Jane Hopper; “Eleven” remains her best-known nickname.
A common mix-up is “Ives,” which is her biological family name, or “Byers,” because she later lives with Joyce Byers and the Byers family. She is also sometimes called simply El, but that is a nickname rather than a surname.