There have been seven ships to serve the US Navy with this name. The first two were commissioned in 1776. One served in the Massachusetts State navy until being captured in 1777. The second served the Continental Navy. She was the first ship of the US, along with USS Ranger, to receive salutes in recognition to the new nation.

The next Indy was commissioned in 1814 and the first true ship of the line for the United States. She was in commission until 1912 when she was broken up in 1915. SP-3676 was the next in line to carry the name Independence. She served from November 1918 until March 1919. Her name was changed and she served until 1946 as an Attack Transport.

Also during World War II there was CVL-22, a light aircraft carrier. She served her country during World War II and was sunk during weapons testing in 1951. The name was applied to another carrier in 1959, CV(A)-62. She served her country until 1998 and is currently in mothballs awaiting her fate.

With the Navy moving in a new direction the name is being used for its newest class of ships, Littoral Combat Ship. USS Independence LCS-2 was delivered in December 2009. She will take the Navy back into the brown water areas. I had the pleasure of seeing her just after she was launched in Mobile Alabama.
Then following these could possibly be

U.S.S. Independence NCC-76704.