Correct, kind of. They don’t use last names tradtionally, and can use “Sherpa” as last name when it’s needed to fit into other culture’s naming schemes.
But they are often given two names at birth (which may be added to or changed later in life): One for the weekday they were born at and a religious or otherwise significant name.
Example: One of the 2 first men to climb everest was Tengzin Norgay. He was born named Namgyal Wangdi. His father’s name was Ghang La Mingma and his mother’s was Dokmo Kinzom.
So in international recognition, his 2 given names are treated as first name and last name.