According to the FAQ in the Apache project website, the name Apache was chosen out of respect to the Native American tribe Apache and its superior skills in warfare and strategy. The name was widely believed to be a pun on A Patchy Server (since it was a set of software patches), but this is erroneous. Official documentation used to give this very explanation of the name,but in a 2000 interview, Brian Behlendorf, one of the creators of Apache, set the record straight:
The name literally came out of the blue. I wish I could say that it was something fantastic, but it was out of the blue. I put it on a page and then a few months later when this project started, I pointed people to this page and said: “Hey, what do you think of that idea?” … Someone said they liked the name and that it was a really good pun. And I was like, “A pun? What do you mean?” He said, “Well, we’re building a server out of a bunch of software patches, right? So it’s a patchy Web server.” I went, “Oh, all right.” … When I thought of the name, no. It just sort of connotated: “Take no prisoners. Be kind of aggressive and kick some ass.”
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.