At no time would you or should you ever have to register or even de-register your Audiobox due to moving it to another computer. Audio Interfaces do not operate this way. Registration of hardware in your user account is for warranty and your personal records. Once registered in your user account, the only reason to remove this registration would be if at some point you were to sell your hardware. This would then allow the new owner to register the hardware in their user account once transfer of ownership has taken place.
Should you be referring to Studio One Software for some reason, rather than hardware... then you have 5 separate activations of Studio One in which you can use on up to 5 computers at once of your choosing.