The name AMD64 is indeed confusing today, but it makes perfect sense if you know the backstory to the name. Back in the 32 bit days everybody realized that 64 bit would be next, just like CPUs had gone from 8 to 16 to 32 bit. Intel started developing 64 bit under the name Itanium while AMD developed 64 bits under the less creative name AMD64. Long story short Itanium didn't really work out, AMD64 had a better solution, at least for consumer computers and Intel ended up licensing the AMD64 extensions. Intel still licenses the base x86 to AMD, which AMD64 builds on top of, which means if you want to build a 64 bit x86 CPU today, you need to license the instructions from both AMD and Intel as they each own different parts of it.
That's why Intel has CPUs with AMD64 instructions. Apple uses it (well used it) too, through I think they consistently called it x86_64.
In short: you shouldn't care if it says you are on AMD64. We all are unless you happen to be using ARM or Apple Metal.
