The site got the name right: Bureau of Alcohol, Tobacco, Firearms and Explosives. There is no descriptive name in front like national, federal, etc in the agency's name. But national is an accurate description of the reach of the BATFE's jurisdiction.
Then the N in National should be lowercase. And in all my years of dealing with guns and the ATF, I've never heard it called national BATF&E. I've heard federal BATF&E many times.