Was the official name Model 3 or Model III?
Model III was the official name, although 3 and III were and are used interchangeably by many people.
The Model I, II, and III were the only three TRS-80 computers to be identified with Roman numerals in the Radio Shack catalogs. Although some pre-release information identified the “Model IV,” the Radio Shack catalogs always used “Model 4.” All future computer models used ordinary numbers.
Presumably, the ever increasing model numbers put a stop to the Roman numeral notation. Thankfully, this spared us the Model II/XII/XVI/VM (2/12/16/6000) business computers and the Model C/CII/CC/DC (100/102/200/600) portables.