No one knows why it's the "Seahawks." Actually, most people don't even know Wagner College. It's a hidden gem.
9 May 1948, New York Times, pg. S4:
Wagner College won its fifth straight game yesterday, crushing the Pratt Institute nine, 9-0, behind the five-hit pitching of Bill Willets at Clove Lakes Park, Staten Island. (...) Seahawk pitchers have not yielded a run in twenty-nine innings.