Determining the model number for a particular hot tub depends largely on the manufacturer. Master Spa hot tubs, for instance, print the year, make and model in the owner's manual provided with the hot tub at the time of purchase.
You can often find a hot tub's model number on the sales agreement or receipt as well. If you cannot find the make, model and year in any of these places, you may be able to contact the manufacturer with the serial number in order to gain the information. Alternatively, the serial number may be printed on a metal tag affixed to the bottom of the tub, behind the front panel or underneath the tub's filter lid.