She was named for Corporal Anthony P. Damato USMC (1922–1944), who was killed in action during the Battle of Eniwetok in the Marshall Islands and posthumously awarded the Medal of Honor.

[1] From her home port at Newport, Rhode Island, and after December 1947, from Norfolk, Virginia, Damato cruised the Atlantic Ocean from Cuba to Newfoundland in training and exercises.

[1] From September to November 1950, Damato had her first tour of duty with the 6th Fleet in the Mediterranean Sea, and during the next year joined in hunter-killer operations in the South Atlantic.

She patrolled off the Levant, then passed through the Suez Canal to join the Middle East Force in the Persian Gulf, returning to Norfolk for local operations in September.

She called at Montréal, at Rochester, New York, and arrived at Toronto for the Canadian National Exhibition, joining in the review of NATO naval forces taken by Admiral of the Fleet, the Earl Mountbatten of Burma, Britain's senior military officer.

On 12 and 13 December 1967, Damato conducted naval gunfire support (NGFS) missions while in the Saigon River[2] and has been placed on the US Veterans Administration list of vessels exposed to agent orange thereby making her crew at that time potentially eligible for certain VA benefits.

Upon returning to Norfolk, VA, it set sail again for the North Atlantic on the western coast of Europe to participate in NATO exercises as a show of force toward the Soviet Union.