Bank Given New Name: The First Women's Bank said it has changed its name--and dropped the gender identification--reflecting a shift in the markets the bank now serves. Effective immediately, the New York bank, founded in 1975, primarily to serve the financial needs of women entrepreneurs, will be known as the First New York Bank for Business. The reason for the switch is that the name First Women's Bank "no longer connoted the direction that our marketing efforts were taking us," said Chairman Martin A. Simon, "It was too confining." The First Women's nomenclature was not entirely set aside, however. It will be retained as the name of a private banking division, and the bank's flagship branch on Park Avenue will continue to bear the First Women's Bank banner.