It is very common to reuse the name of a ship in the Navy. Even when the previous one was lost in combat.
Here are just some examples:
USS Chicago (CA-29) Heavy Cruiser - sunk at the Battle of Rennell Island in 1943
USS Chicago (CA-146) Heavy Cruiser 1945 - 1984
USS Chicago (SSN-721) Nuclear Attack Submarine 1986 - present
USS Yorktown (CV-5) Aircraft carrier sunk in 1942
USS Yorktown (CV-10) Aircraft carrier commissioned in 1943 - now a museum
USS Yorktown (CG-48) Cruiser commissioned in 1984 - slated to be scrapped
USS Wasp (CV-7) Aircraft carrier built in 1936 and sunk in 1942
USS Wasp (CV-18) Aircraft carrier 1943 - 1972
USS Wasp (LHD-1) Amphibious assualt ship 1989 - present
USS Lexington (CV-2) Aircraft carrier sunk in 1942
USS Lexington (CV-16) Aircraft carrier 1943-1991
USS Aaron Ward (DD-483) 1942 - sunk in 1943
USS Aaron Ward (DM-34) 1944-1945
USS Princeton (CVL-23) Sunk at Leyte Gulf in 1944
USS Princeton (CV-37) 1945 - 1970
USS Princeton (CG-59) 1989 - present
USS Barton (DD-559) Destroyer sunk in 1942
USS Barton (DD-722) Destroyer 1943-1968
USS Helena (CL-50) Light Cruiser 1939 - sunk at the Battle of Kula Gulf in 1943
USS Helena (CA-75) Heavy Cruiser 1945 - 1964
USS Helena (SSN-725) Nuclear Attack Submarine 1987 - present
For many more examples, go to this page:
http://www.history.navy.mil/faqs/faq82-1.htm
(A history of ships sunk or damaged beyond repair in WWII)
and search for the name of any ship listed as sunk on that list - you will find that a majority the names were reused on other ships.