The name of this planet was not verbally referenced on screen. A legible version of the okudagram, in which the name was seen, first appeared in the reference book, Star Trek: The Next Generation - The Continuing Mission, before it was seen in the remastered version of the episode.
"Planet 10" was an in-joke reference to the film The Adventures of Buckaroo Banzai Across the Eighth Dimension!, with "DIM-8" being an abbreviation for the "8th Dimension."
According to ENT: "Two Days and Two Nights", prior to 2151, Earth ships had been operating within 90 light years of the Sol system. In that year, the Enterprise became the first ship to travel further than this distance. With the planet being visited in 2137, Planet 10 (DIM-8) was presumably located within this range.