Like all of Super Hero Island, this shop doesn't have a specific name out front. It is, simply, "Shop". Once you peek in, however, it's impossible to miss who this store is dedicated to. The walls sport sleek images of Spidey swinging through town, and all of the pieces in the shop are adorned with his image or logo.
You'll exit through the Spider-Man Shop after you ride The Amazing Adventures of Spider-Man but even visitors too small for the attraction will find this location worth a look.
If you want to meet Spider-Man in the flesh, head across the street to the Marvel Alterniverse Store where he stops for meet and greets.