Stella Mudd's planet was an otherwise unnamed class M planet in or near Federation space of the galaxy's Alpha or Beta Quadrant. (TOS - Mudd's Angels short story: "The Business, As Usual, During Altercations")
History and specifics
In 2270, after Harry had been apprehended at Starbase 7, the Federation allowed Mudd to return home while legal action was being considered. Leonard McCoy suggested he be taken to Stella Mudd rather than to the planet Mudd. Harry was unwilling to provide the planet's coordinates except through hypnosis.
The starship USS Enterprise orbited the planet while James T. Kirk, McCoy, Yeoman Weinberg and two security guards escorted Harry to the residence. However, the landing party was ordered to leave and threatened with a shotgun, so they hastily retreated to the Enterprise, and Mudd was taken to Mudd's planet instead. (TOS - Mudd's Angels short story: "The Business, As Usual, During Altercations")