1) US Army installations are “forts”, not “bases”, when located in the US. The one you referenced was named Fort Bragg, home of the Infantry.
2) While it was not my personal privilege to know General Moore, my sense of his concept of an officer’s honor makes me wonder if he would have declined the attachment of his name in place of Bragg. JMO…YMMV
Fort Bragg is now Fort Liberty.
I should be more precise in my use of language.