When I have watched Rick And Morty I have never figured out if Morty's name is actually Mortimer and it is never mentioned throughout the show. I do know that Morty is indeed short for Mortimer and so it makes me think that Morty is named Mortimer Smith
Bestie

Could be Morton.

Mortimer "Morty" Smith (voiced by Justin Roiland) is Rick's neurotic 14-year-old grandson who is frequently dragged into Rick's misadventures.
Hi, Bestie! Did you know that Morty became a gir named Morticia on an episode?
DTK