Spider-Man: Far From Home refers to Spidey in his stealth suit as Night Monkey, but is this actually taken from the pages of Marvel Comics?
Borrowing from my answer to this question over on SFF:
As far as I can tell Night Monkey is an entirely new creation for the film and there is no previous character with the same name. Executive producer Eric Carroll has spoken about the design for the suit and its inspiration but doesn't mention the name.
While this particular stealth suit is a new creation for the MCU, drawing on the visual language established by the movies already, it does have some notable comic inspirations. “It’s inspired by a bunch of different looks in the comics,” executive producer Eric Carroll noted. “We have Noir, Big Time—but of course, when Ryan [Meinerding, concept artist and Marvel Studios head of visual development] was designing this, he has all the past SHIELD agents in mind, so it’s very reminiscent of what a Black Widow or Hawkeye wear. And it’s got all these little details, which Ryan’s amazing at.”
That said there is a character named Hit Monkey that first appears in a Spider-Man. Deadpool team up. However, this does not appear to be the inspiration for the name.
As mentioned in the comments there is also Spider-Monkey but like Hit Monkey he doesn't appear to be the inspiration for the name. You can see him in the below panel from Superior Spider-Man Vol 1 issue 32 alongside Spider-Man Noir.
If you want a bit of a stretch the night part could come from Nightcrawler as Spider-Man has interacted with him a bit in the past. And if you want to stretch that theory even further Jake Gyllenhaal starred in a film of the same name but it is unrelated to Marvel as far as I know.
Whilst your question was only about the naming of the character it is worth pointing out that the costume/suit appears to be influenced from Spider-Man Noir.