It's complicated, but modern processors actually do have many more registers than you can name in the instructions. They use things like "register renaming" to

It's complicated, but modern processors actually do have many more registers than you can name in the instructions. They use things like "register renaming" to avoid false conflicts between instructions. Registers that you name in assembly != physical registers. And when you use a register in two different instructions, you won't necessarily get the same physical register each time.