So for this one we can actually get an answer right from the Army! http://www.history.army.mil/html/faq/base_name.html

For much of the Army's history in the 19th Century, the naming of posts was still mainly a local prerogative. For example, War Department General Order Number 79, dated 8 November 1878, left the naming of installations to the commander of the regional Military Division in which the installation was located. Although not always, the names of installations usually reflected a local influence, such as Fort Apache in Arizona, established in 1871, and the Chickamauga Post in Georgia, established in 1902. In the 1890s, the then Quartermaster General, Maj. Gen. Richard N. Batchelder, recommended that the War Department assume responsibility for naming installations, but that did not become policy until World War I when the massive general mobilization saw the establishment of numerous installations of various sizes and functions. The names usually, but not always, reflected some regional connection to its location, and usually with a historic military figure significant to the area: for example, Camp Lee near Richmond, Virginia, and changing the name of the Chickamauga Post in Georgia to Fort Oglethorpe.

In the years between the World Wars, it became the common practice for the War Department to entertain recommended names for posts from installation commanders, corps and branch commanders, and the Historical Section Army War College, as well as from outside the Army. Public opinion and political Influence sometime weighed heavily on the decisions. For an example of the latter, when in 1928 the Army renamed Fort George G. Meade in Maryland as Fort Leonard Wood, the Pennsylvania delegation in Congress held up the Army's appropriation bill until the service agreed to restore the name of the Pennsylvania-born general. The regional connection, however, cannot be overemphasized. Fort Monmouth in New Jersey, for example, was originally named Camp Alfred Vail, in honor of the Army's then chief Signal Officer, when the installation was established as a Signal Corps training facility in 1917, but changed to Fort Monmouth, for the 1778 battle fought nearby, when it became a permanent installation in the 1920s.

The War Department better defined the criteria when it established the policy for "naming military reservations in honor of deceased distinguished officers regardless of the arm or service in which they have served" in a memorandum dated 20 November 1939.

So it was mostly up to the local district and post commanders to select names when appropriate with varying levels of oversight from above, and it allowed for the smoothing over of any local opposition to the ever expanding bases.

In general the US military has been remarkably willing to adopt the names of former foes as marks of esteem or of distinction. From CSA officer's with Forts named for them to the very names of vehicles. The fact that KIOWA, BLACKHAWK, IROQUOIS, COMANCHE, and APACHE have all been used is testament to that.