Spider-Man: Homecoming has two major supporting characters: Ned, Peter's best friend, and Liz, his crush. I didn't recognize either of these names. Do they have equivalents in the Spider-Man comics involving Peter Parker?
There are characters named Ned and Liz from the comics who the film characters seem to be in part or fully based on.
Liz Allan was a high school classmate of Peter's in the early issues, a sometimes-girlfriend of Flash Thompson and also love interest for Peter himself. Typically in adaptations, she's replaced by Gwen Stacy or Mary-Jane Watson, in order to streamline the storyline (both are more iconic love interests, but he didn't meet either until college).
Ned Leeds was a fellow reporter at the Daily Bugle, and not a classmate at all. It seems the character Ned in the movie is partly inspired by him, but is also an amalgamation of various other Spider-Man supporting characters. This article cites the Co-producer and director of development for Marvel Eric Carroll:
Peter’s friend Ned (played by Jacob Batalon) didn’t have a last name in the script. While Ned Leeds is a well-known character from the Spider-Man universe, the filmmakers only started with Leeds when building out Homecoming’s Ned but they essentially created their own character with him. Carroll said that he and other characters in the film are essentially composites of several of their favorite players from the Spidey comics, and while Ned may eventually wind up with the last name “Leeds,” that is not a guarantee.
One of the characters Ned is heavily inspired by seems to be Ganke Lee from the Ultimate Spider-Man comics, not a supporting cast member of Peter Parker at all, but rather of Miles Morales (who replaced him in that universe). In addition to the visual look of the character,
the plot where
Ned learns that his friend is Spider-Man
more closely echoes plots in Ultimate Spider-Man than anything in the Peter Parker comics, where
very few people learn his identity, especially in high school, and live to keep the secret.
Bit more info on Liz Allan and Ned Leeds from the comics.
Liz Allan may have occasionally shown an interest in Peter, and he may have reciprocated slightly, but his real early romantic interest was Betty Brant.
Peter didn't keep up with Liz following high school. She appeared years later (AMAZING SPIDER-MAN circa 132), where we found out her brother is a villain called the Molten Man.
Shortly thereafter, she met Harry Osborn (who was recovering from a mental break, when he discovered his late (at that time) father Norman was the Green Goblin, and took over the role for a short time). Harry and Liz ultimately got married, and had a kid (Norman, usually called Normie). Things get a little confused, from there: Harry died (he got better too), Liz took over Oscorp, then suddenly Norman was alive again, took over the company again, and Liz was pretty much shuffled off to the side. Most recently we've seen her running a different company, Alchemax (see SPIDER-MAN 2099).
Ned showed up as a reporter for the Bugle, and showed an interest in Betty around the time Peter moved on to college. Ned and Betty were seen occasionally, but weren't terribly active as supporting cast members. He and Betty got married (AMAZING SPIDER-MAN 156), had some marital issues almost immediately (Betty was back and trying to start something with Peter around AMAZING SPIDER-MAN 182 or thereabouts). Betty eventually became a reported herself, and stayed married to Ned (I think until his death), though she had a relationship with Flash Thompson towards the end of that time.
Ned ultimately was killed near the climax of the original Hobgoblin saga. He died in SPIDER-MAN VS WOLVERINE in the late 1980s. He was believed to have been the Hobgoblin at one point, though I think he was cleared fairly quickly. Ultimately (years later), we found out that the Hobgoblin had been Roderick Kingsley.
You'll note that there's not much about Ned in here. Peter and Ned Leeds weren't particularly close - he was someone else who worked at the Bugle, and was basically a friend of a friend.