Having many Trek "moons" be substantially larger than Luna and orbiting a gas giant would explain how a moon would hold an atmosphere, their 1 G or thereabouts gravity, and other things, but they are still called moons. And having multiple habitable moons around the same gas giant might sometimes explain why some cultures that are barely space-capable are visiting their "next door" neighbors. In the remastered TOS episodes, Starbase 11 appears to be on such a moon orbiting a gas giant (
The Menagerie, Part 1 and
Court Martial).
However, the planet Vulcan is always called a planet and never a moon, and that's a fairly important distinction to astronomers and astrophysicists. In
TMP, they showed two orbs in the sky, IIRC, but they took those out in the director's version, though they claim it was not to comply with the "no moon" dialogue from
The Man Trap but for other reasons.
Some now say Vulcan has a sister planet (but from
TMP, if it has any validity, it would have to have two or more sister planets, and the stability of such a system is in doubt when they are that close together (unlike earth's sister, Venus, which is so far away it looks like a bright star, or Mars, not a sister but also looks like a star). But a binary planet (two planets orbiting one another and close enough to see each other as discs in the sky) may be possible and stable (so the theatrical release of
TMP is still a problem, but the director's cut is fine). But hardly anyone official wants to give definitive answers to these sorts of things.