The other NYC bridges are all (I think?) named Bridge, but they went with Crossing here because Outerbridge Bridge sounds weird.
Another NYC one: A lot of people think "major" in The Major Deegan Expressway means it is a significant expressway, but actually the expressway is named after (Army) Major William Deegan
Maybe I'm weird but I think NYC area has numerous semi-poetic sounding roads (while most of the country just uses route numbers): Harlem River Drive, Cross Bronx, Major Deegan, Van Wyck, Belt Parkway, Grand Central Parkway, the Taconic, Palisades Parkway, the B.Q.E., the Sprain Brook. Plus the Verrazano and Tappan Zee.
Houston does the same with its highways, and, in fact, they have different names depending on their relation to downtown. For example, I-45 is both the Gulf Freeway and North Freeway, 59 is both Eastex and Southwest.
Austin also has named highways (Mopac, Capital of Texas, Research), except I-35, which I was once told was because "it was the only one not created locally."
Context for non-New Yorkers: Outerbridge is the southernmost bridge in NYC and New York State, and Staten Island might as well be on Mars for the rest of the city. So the name "Outerbridge" is all the more fitting (and surprising).
The George Washington Bridge and Outerbridge Crossing both connect New York City (on the east) with New Jersey (on the west) but are about 45 minutes apart, even with no traffic.