The naming convention has been in common usage forever in science fiction. E.E. Smith from the first Galactic Patrol serial in 1937 referred to planets such as Velantia III, Rigel IV, and Palain VII, and Earth was specifically referred to as Sol Three from time to time in the series.
The following examples are from Galactic Patrol:
"For instance, Kinnison here once had a highly adventurous interview with a lady of Aldebaran II and her friends."
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"Kimball Kinnison of Sol Three calling Mentor of Arisia. Is it permitted that I approach your planet?"
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"Kinnison of Tellus, greetings. Tregonsee of Rigel IV calling from Trenco space-port. Have you ever landed on this planet before?"
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"Lensman of Trenco Space-port--Tregonsee or his relief? Lensman Kinnison of Sol III asking permission to land."
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"....the fifth dove into the deepest ocean of Corvina II, in the depths of which all rays are useless."
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Out from Radelix and into deep space shot the speedster, bearing the Gray Lensman toward Boyssia II, where the Boskonian base was situated.
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"He was Lageston of Mercator V--a good man, too. What is your pressure now?"
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Addendum
One should note that at no point does Smith explain that "Sol III" means "third planet from the star Sol" or Aldebaran II means "second planet from the star Aldebaran". This implies one of two things: either Smith used it for the very first time and expected the readers to figure out what it meant without explanation--which given Smith's writing style would seem to be unlikely since he tends to explain everything--or the style of naming planets in that way was already in science fiction at the time so as not to require explanation.
