What is the last name of Dexter's biological mother?

Dexter’s biological mother’s last name is Moser.

In the television series, she is identified as Laura Moser, also called Laura Lynn Moser. She was involved in the drug trade and later worked as a police informant connected to Harry Morgan. When her criminal associates discovered her cooperation with the police, they murdered her in a shipping container while her sons, Dexter and Brian, were present.

That traumatic event becomes the origin of both brothers’ later violence and is one of the central pieces of Dexter’s backstory. Dexter is eventually adopted by Harry and Doris Morgan, which explains why he uses Morgan rather than Moser as his surname.

A frequent mix-up is answering Morgan because Dexter’s adoptive family gave him that name. Bennett belongs to Rita’s family, while Driscoll is the surname of Dexter’s biological father, Joe. The television continuity specifically establishes Laura’s surname as Moser.