You're confusing instruction-set architecture with micro-architecture. The x86-64 ISA defines 16 integer ("logical") registers, for example, however, Skylake h

You're confusing instruction-set architecture with micro-architecture. The x86-64 ISA defines 16 integer ("logical") registers, for example, however, Skylake has (don't quote me on the figure) 168 physical integer registers. For register renaming to work, you need more physical registers than logical registers because the logical registers need to be mapped to some physical registers, possibly multiple times (e.g. for speculation).