The first new Continental Navy ship was "Alfred". This warship was named in honor of Alfred the Great, who was the king of Wessex and was credited with building the first English naval force. Another ship was named "Raleigh", in commemoration of the seagoing exploits of Sir Walter Raleigh. These names of the Navy warships, traces its ancestry to 13 October 1775.
Do you mean the first ship that sailed under a United States flag after independence was declared? If so, there were a few, but the most famous was the ship commanded by John Paul Jones . . . the "Serapis". There may have been earlier ships pressed into service in our first naval fleet, but his was most notable at the time . . . look up the other ships names to see if another one pre-dates the Serapis.