The 300 sailors on each ship will take part in maritime security operations and conduct exercises with ships of allied navies over the next seven months, according to the U.S. Navy.
Kidd was the commander of Battleship Division 1 at the time, which also included the USS Nevada and USS Pennsylvania. The Arizona was his flagship.
The Pinckney is named for Cook First Class William Pinckney, a World War II combat veteran who received the Navy Cross for his rescue of a fellow crew member on board the aircraft carrier USS Enterprise during the Battle of Santa Cruz in October 1942.
According to the Navy, Pinckney was at his battle station in an ammunition handling room aboard the Enterprise when the carrier was struck by two Japanese bombs. He and another sailor were the only ones who survived among a group of six.
When the other sailor collapsed, Pinckney carried the larger man to safety through flames, suffocating smoke and gasoline fumes, according to the Navy. He was one of only four blacks to receive the Navy Cross during the war.