The mummy’s name was Im-Ho-Tep, aka Ardeth Bey, played by Boris Karloff.
In the four sequels that followed, The Mummy’s Hand (1940), The Mummy’s Tomb (1942), The Mummy’s Ghost (1944), and The Mummy’s Curse (1944), the mummy’s name was Kharis.
Western star Tom Tyler played Kharis in the first of the sequels; Lon Chaney, Jr., in the others.