The Old Man Logan character has since joined the main timeline of Marvel Comics proper, replacing his dead mainstream counterpart right on time for his movie.
Logan is very loosely based on the popular comic book storyline “Old Man Logan”.
It’s a nice little shout out from Logan to one of its main inspirations…unless Logan is just calling himself that with zero self-awareness.
It does, however, throw in a little reference for fans of Wolverine when Logan calls himself an “old man.”