Is the correct 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.