AMD developed the architecture and lobbied for that name heavily for marketing reasons.
Before Intel's use of the architecture became well established, it looked like that lobbying might work. Intel's branding was a mess--they actually had two variations, IA32e and EM64T, and have since come up with even more names. Even Microsoft was using "AMD64":
The thread where apt/Debian decided on the name contains a lot of data about what names other lower-level tools were using at the time:
Personally, I prefer x86_64 over amd64 or x64, but eh.