The coroner's office identified the victim as 55-year-old Washi Uddin Ahmed of North Hollywood.
There's a growing memorial at the 7-Eleven in Valley Village, where Ahmed and his wife were attacked on Friday.
Surveillance video shows the victims confronting the robbery suspect over a stolen sandwich and bottle of liquor.
Ahmed was stabbed in the neck and succumbed to injuries. His wife was stabbed twice. An update on her condition was not available.
A homeless parolee is being held without bail in connection with the crime.