USS Gregory (DD-802) was one of the Navy's Fletcher-class destroyers. The name honored Rear Admiral Francis H. Gregory (1780–1866), whose career at sea began in the War of 1812 and continued into the Civil War. This hull was the second Navy ship to carry that name.
She was launched on 8 May 1944 and commissioned on 29 July 1944. Captain Bruce McCandless commanded her from that day until 9 October 1945, when Captain Wayne Mowrer Newport took over. Gregory survived the war.
With the fighting over she was kept at San Diego in an inactive reserve status while still in commission, then decommissioned on 15 January 1947. She returned to commission on 27 April 1951. In her later active years she received the Battle Efficiency E for 1955, for 1956, and again for 1959. On 1 February 1964 she was decommissioned at San Diego and placed in reserve once more.
On 1 May 1966 her name was removed from the Navy List. Under the new name Indoctrinator she stayed at San Diego as a moored training ship from 20 May 1966 until 8 January 1971. On 4 March 1971 the hull was put aground at San Clemente Island, off Southern California, and sunk as a target.