She was named for Marine Private Joseph W. Ozbourn (1919–1944), who was awarded the Medal of Honor posthumously for his "great personal valor" during the Battle of Tinian.

Although two crew members were killed, damage control parties saved the ship, and she returned to Long Beach Naval Shipyard for repairs.

During 1949 and early 1950, Ozbourn trained midshipmen, underwent overhaul and participated in various exercises, one of which was the first guided missile test at sea conducted with Norton Sound.

In February 1951, despite having received two direct hits and several near misses from shore batteries the same day, Ozbourn sent her motor whale boat to rescue a downed pilot floating in a mine field.

From 1956 to 1964 Ozbourn underwent major overhaul, engaged in intensive training exercises, participated in festivals and celebrations in several west-coast cities and in Australia, and operated periodically with the 7th Fleet.

Having undergone Fleet Rehabilitation and Modernization (FRAM) Mark I conversion earlier, she joined Task Group (TG 10) for a major Presidential Demonstration.

Ozbourn sailed independently for Pearl Harbor 8 July 1964 to join DesDiv 233 and ASW Group 1 for a six-month Western Pacific deployment.

From Yokosuka, Japan, ASW Group I sailed for the South China Sea after North Vietnamese PT boats had engaged American destroyers in the Gulf of Tonkin.

After providing antisubmarine warfare (ASW) protection for TF 77 and after participating in a naval weapons demonstration, Ozbourn returned to Long Beach.

Attached to TG 77.6, Ozbourn provided gunfire support in the III and IV Corps areas of South Vietnam delivering tons of high explosives in covering fire.

For "outstanding actions against the enemy and for excellent combat readiness", she received both the Meritorious Unit Commendation and the Battle Efficiency "E".

On 17 June Ozbourn left Long Beach on a midshipman cruise to San Francisco, Seattle and Tacoma, Washington, and Pearl Harbor.