In the book Mort, the character is indeed called Mortimer, which gets shortened to Mort. There's a bit when Death and Mort first meet:
Death is acknowledging that in some languages he is known as Mort, or in countries where words have sex - Morte.
WHAT IS YOUR NAME?
'Uh,' said Mort, 'Mortimer ... sir. They call me Mort.'
WHAT A COINCIDENCE
'Uh,' said Mort, 'Mortimer ... sir. They call me Mort.'
WHAT A COINCIDENCE