It appears to be a fairly common planetary naming scheme in science fiction: Take the common name (or its bayer designation) of star and append the planetary ordinal in the form of a Roman or Arabic numeral.

Examples

• Earth becomes Sol Ⅲ
• The tenth planet of Pollux becomes Pollux Ⅹ
• The forth Planet of Beta Hydri becomes Beta Hydri Ⅳ

It's not based in reality

I asked an astronomer and he assured me, no astronomer ever proposed such a naming system.

Real exoplanets today are named using an entirely different naming scheme.

Who came up with it?

It is very common in Star Trek, but it exitsted in earlier science fiction novels and short stories. What is the earliest occurrence of this naming scheme? When was it first described? When was it first implied?