How does a number is saved in a register
Registers don't have endianness. Endianness is only relevant when data is stored in memory.

The reason endianness is relevant to memory is because you can access the individual bytes of memory, using an address. You generally can't access the individual bytes of a register, and when you can, they have names (like %al is "the lowest byte of %rax") which mean the same thing regardless of endianness.

If you couldn't access individual bytes from memory, or if you used a command like "get me the lowest byte of address 5" instead of "get me address 20", then endianness wouldn't matter for memory either.