The costume and nickname (Jewel) suggested by Trish are from the original comic.
In New York, another name for a submarine sandwich is a "Hero Sandwich". The fact that Jessica dressed up as a hero sandwich in one of her odd jobs is a pun on the fact she is a "hero".
In the flashback, when Jessica meets Kilgrave for the first time, he asks her for her name and, when she responds with Jessica Jones, he asks her for her superhero name. She claims she doesn't have one. This directly contradicts the comics version. There Kilgrave meets Jessica as Jewel and, when asked for her name, Jessica responds, "Jewel". Kilgrave then asks for her real name, to which she responds "Jessica".
When Jessica, Trish and Will are preparing to capture Kilgrave, Will can be seen sitting on a park bench reading a newspaper with a headline mentioning Costa Verde. Costa Verde is a fictional Central American republic from the Marvel comic universe, with a turbulent history. It's most famous citizen is the superhero Silverclaw, who at one point is a member of the Avengers in the comics.
In one scene, a kid dressed as Captain America can be seen walking through a park.