Many people think the name of this bridge is the Outer Bridge, because it is on the outer reaches of Staten Island and NYC.  However, it was named after Eugenius Harvey Outerbridge who was the first chairman of the Port Authority of New York and was a Staten Island resident. (I guess the Outerbridge Bridge would sound too odd.)

http://en.wikipedia.org/wiki/Outerbridge_Crossing

The Staten Island side of the bridge is actually in Richmond Valley, the next town to Tottenville, and links the island to Perth Amboy, New Jersey continuing Route 440 which also goes through Staten Island. The bridge opened on June 29, 1928.

Mr. Outerbridge’s sister, Mary, is credited with importing the game of tennis to the United States, with the first game being played at the Staten Island Cricket Club

http://en.wikipedia.org/wiki/Mary_Ewing_Outerbridge