[cesarb]

It's not just the article title. Follow the two footnotes in the "History" section of that article, to the press releases from AMD announcing the new ISA. They consistently call it "AMD x86-64" or "AMD's x86-64" or just "x86-64". The oldest snapshot I could find of the x86-64 web site (https://web.archive.org/web/20000817014037/http://www.x86-64...) also calls it x86-64. The most recent snapshot of that site, however, calls it AMD64; it seems to have changed sometime in the middle of April 2003.

That is, both x86-64 and AMD64 are historically accurate (2003 was early enough in the ISA's lifetime), but x86-64 is the earlier name.