The Book of Judges has a strange phenomenon: there are characters who crop up, and they share the same names with their places of residence and people from the Book of Numbers.
First of all, there's Jair. In Judges 10:3-4, we read that Jair was a judge from Gilead, whose well-off sons lived in Havvoth-Jair.
But Jair is first mentioned in Numbers 32:40-41: "so Moses gave Gilead to Machir son of Manasseh, and he settled there. Jair son of Manasseh went and captured their villages, and renamed them Havvoth-jair" (NRSV). In one tradition, Jair seems to live in the time of Moses, since he was taking the Transjordanean land that Moses permitted to the half tribe of Manasseh (Joshua 13:30).
Second, there's Gilead. Gilead is the father of Jephthah, and he lives in (you guessed it) Gilead (Judges 11:1-2). Now, with Jair, you can probably make the case that him being the "son of Manasseh" means he's just descended from Manasseh, instead of being a direct son (see I Chronicles 2:22-23). But you really can't say that about Gilead, since Judges 11:1-2 says that Gilead had Jephthah with a prostitute.
And Gilead also shows up in Numbers. According to Numbers 26:29, Gilead was Manasseh's grandson. And he too is associated with (guess where?) the land of Gilead.
The problem is that we can't assume that Jair and Gilead lived for three hundred years, the approximate time between the Israelite conquest of Canaan and the period of the Judges (see Judges 11:26). These weren't the days of Methuseleh! Moses died at age 120 (Deuteronomy 34:7), and Caleb thought he was old when he was 85 (Joshua 14:10).
One solution is to say that they're different people. And that's plausible, for there are many people who have the same name. Plus, Luke 1:61 records the Jewish custom of naming people after relatives. And so if a woman who lives in Gilead has a son, what better name is there for him than "Gilead"?
But could it be that there are different traditions about the same person? In the movie Big Fish, a man tells his son tall tales that are based on his own experiences. One story is about a witch he encountered when he was a kid. He looked in the witch's eye and saw his future death, and that gave him comfort throughout his life (since he knew how he'd go). Well, it turns out that he had some of his details mixed up, for the witch was actually a woman he met in his adulthood. And she was not a witch when he first met her--she just degenerated to that point long after he helped her (and rejected her advances). And so the man had a single character in his mind, but he placed her in the wrong time frame.
Could there have been different stories about the founders of Gilead and Havvoth-Jair? I don't know. One argument against that is there are parts of Judges that presume the Conquest stories. Jephthah mentions a few of them to the king of Ammon in Judges 11. So it would make sense that the author/compiler of Judges believes that the Israelites took the land of Canaan in the Conquest. And that would include Jair and Gilead's taking of the Transjordan.