The following excerpt is from the Navy Historical Center. The full text can be located at:
http://www.history.navy.mil/faqs/faq63-1.htm
After World War II aircraft carriers were given a mix of such traditional carrier names as Ranger, Saratoga, and Coral Sea and names of individuals. The first of these, as we have seen, was Franklin D. Roosevelt, later followed by Forrestal and John F. Kennedy. All the ships of the current Nimitz class bear the names of such national figures as Theodore Roosevelt, George Washington, and Ronald Reagan.
As with many other things, the procedures and practices involved in Navy ship naming are as much, if not more, products of evolution and tradition than of legislation. As we have seen, the names for new ships are personally decided by the Secretary of the Navy. The Secretary can rely on many sources to help him reach his decisions.
Each year, the Naval Historical Center compiles primary and alternate ship name recommendations and forwards these to the Chief of Naval Operations by way of the chain of command. These recommendations are the result of research into the history of the Navy and by suggestions submitted by service members, Navy veterans, and the public. Ship name source records at the Historical Center reflect the wide variety of name sources that have been used in the past, particularly since World War I.
Ship name recommendations are conditioned by such factors as the name categories for ship types now being built, as approved by the Secretary of the Navy; the distribution of geographic names of ships of the Fleet; names borne by previous ships which distinguished themselves in service; names recommended by individuals and groups; and names of naval leaders, national figures, and deceased members of the Navy and Marine Corps who have been honored for heroism in war or for extraordinary achievement in peace.
In its final form, after consideration at the various levels of command, the Chief of Naval Operations signs the memorandum recommending names for the current year's building program and sends it to the Secretary of the Navy. The Secretary considers these nominations, along with others he receives as well as his own thoughts in this matter. At appropriate times, he selects names for specific ships and announces them.
While there is no set time for assigning a name, it is customarily done before the ship is christened. The ship's sponsor--the person who will christen the ship--is also selected and invited by the Secretary. In the case of ships named for individuals, an effort is made to identify the eldest living direct female descendant of that individual to perform the role of ship's sponsor. For ships with other name sources, it is customary to honor the wives of senior naval officers or public officials.