Given that Phillip Jeffries declined to talk about Judy, or even identify her, her identity has been the subject of much speculation over the years. The name Judy occurs once in the series under unusual circumstances, after Major Garland Briggs has been kidnapped and drugged by Windom Earle. As he later recovers at the sheriff's station, he seems not to recognize his name and questioningly replies "Judy Garland?" However, it should be remembered that this was the name of the actress who played Dorothy in The Wizard of Oz (which was heavily referenced in Lynch's then-most recent feature, Wild at Heart), and probably not meant as a reference to a character in the later film.
In the recently released feature The Missing Pieces from the Twin Peaks Blu-ray set, a longer version of the Phillip Jeffries scene is found, which contains a few additional clues. Jeffries is seen checking into a hotel in Buenos Aires, whereupon the hotel clerk gives him a letter left for him by Judy. Later, when he mysteriously appears at FBI headquarters, his line "I found something...and then there they were" is expanded into "I found something, in Seattle, at Judy's...and then there they were." The scene as it appears in the finished film is intercut with the scene of the various otherworldly characters (such as BOB and the Man From Another Place) in such a way as to imply that these beings are the "they" of which Jeffries is speaking. One could therefore infer from the longer version of the dialogue that the convenience store was in some way connected to Judy. It is uncertain if Lynch considers the Missing Pieces to be canonical.
In an interview with the Twin Peaks fanzine Wrapped in Plastic, co-writer Robert Engels stated that Judy was meant to have been Josie Packard's sister, who was involved in dealings with Agent Jeffries and ex-Agent Windom Earle in Buenos Aires. This plot thread would have apparently been expanded upon had there ever been any subsequent Twin Peaks movies.
In the 2017 series, Twin Peaks: The Return, episode 17, Gordon Cole revealed that Judy was a corrupted form of the older name "Jowday," which he described as a "strong negative force." Jeffries had become aware of this entity prior to his disappearance. Later, Major Briggs contacted Cole in reference to this being, and the two of them, along with Agent Cooper, put together a plan to find Judy. It is not clear if Cole knew at the time that the entity Briggs named as Jowday was the same being Jeffries was referencing previously, or if he made the connection later. While not confirmed in the series, the ghostly creature seen in the first episode of The Return (along with a few subsequent appearances) is suspected by many viewers as being Judy.