It's been a long time since I've looked at that map. I think I have a copy on this site as well.
It's really interesting that Ongs shows up, but Toms River is nowehere to be seen.
I would imagine that Ongs would have been named for a family of Ongs living in the area, and perhaps one of them started a tavern with a sign that had a hat on it. (Since most taverns advertised themselves with pictoral signs back then.)
Since I have heard & read so darned many versions of the naming and origins here... & I have originally poked around this site because it appeared highly informative with so much input,
Which is it?