The ship was named in honor of Hershel W. "Woody" Williams in an announcement by then-Secretary of the Navy Ray Mabus, on 14 January 2016.

[11] The $498 million contract for the then-unnamed vessel was awarded to the National Steel and Shipbuilding Company (NASSCO), a division of General Dynamics, in December 2014.

[16][17] Hershel “Woody” Williams, while with the U.S. Sixth Fleet, visited Cape Town, South Africa in February 2021,[18] and again in August 2022.

[19] On 28 February 2023, Hershel “Woody” Williams arrived in Mersin, Turkey to deliver relief supplies for those affected by the 2023 Turkey-Syria earthquake.

[21] On 3 June 2024, Hershel "Woody" Williams made its first visit to the port of Malaga to complete a rest call.