The Apache group was formed around a number of people who provided patch files that had been written for NCSA httpd 1.3. The result after combining them was A PAtCHy server.
Yes, it clearly states that on a snapshot of their old web site. They are now going around and changing that information on current web sites. Hence the cries of "revisionist". In fact, their current site says that the "A PAtCHy" version is incorrect, in spite of the snapshot you linked.
"Secondarily, and more popularly (though incorrectly) accepted, it's a considered cute name which stuck. Apache is "A PAtCHy server"."