The name of this planet appeared on an okudagram that appeared on Jean-Luc Picard's desk monitor, and was not verbally referenced on screen. A legible version of the okudagram appeared in the reference book, Star Trek: The Next Generation - The Continuing Mission.
"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."
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. (ENT: "Two Days and Two Nights")