amd64 was an attempt to "brand" the 64-bit version of x86, just as ia32 was an attempt to "brand" the 32-bit version of x86. Many people rejected both and just say x86 and x86-64 as generic names.
The "64-bit version of x86" is actually the new ISA created by AMD that was backwards compatible with x86 and added a 64-bit mode.
I'm sure that you agree that the company that creates a ISA has the right to name it.