The Pasuk already listed the chiefs of Esav earlier in the Perek! Moreover, the current list does not tally with the previous one!
Rashi: This list, of the chiefs who ruled after the death of the last king, Hadar, 1 are actually names of the regions where they ruled.
Rashbam: The chiefs listed here eventually ruled over their respective cities, as is explained in Divrei ha'Yamim.
Ramban: The chiefs mentioned above all ruled together in the same city. Those mentioned here, each ruled by himself over all families of Esav, like a king, but did not have the majesty of a king. 2
Malbim (to Divrei ha'Yamim I 1:43): There were always 11 chiefs that ruled Edom with the king at their head.
Rashi: As is explained in Divrei ha'Yamim I 1:51. Ramban - as a matter of fact, the Torah presents three eras regarding the rulers of Edom: (a) that of the chieftains of the first generation; (b) that of the kings and (c) that of the chieftains that followed (Refer to 36:40:3:2).
Ramban: The 10 chiefs mentioned here hint at the ten kings that would rule over Edom, (all part of the fourth Malchus that would subjugate Yisrael), the last one being Rome. After that, their sovereignty will spread over the entire world. Daniel (7:24) alludes to this.
What is the significance of the phrase "l'Mishpechosam, li'Mekomosam, bi'Shemosam"?
Ramban #1: In conjunction with "l'Moshevosam b'Eretz Achuzasam" (in 36:43), it teaches us that, opposed to the previous list, where they all ruled simultaneously in the same city (much like the princes of the 12 tribes), the chiefs mentioned here ruled one a time, each one over all the families of Esav, and over all the lands that pertained to Edom. 1
Ramban #2: Li'Mekomosam teaches that they ruled simultaneously, each one over his own region. Ha'amek Davar - Eretz Edom was divided into regions with these names.
And it was only after the one died that his successor took over.
When did these chiefs rule?
Ramban #1: Many say that this is a prophecy (they will rule after the Torah was given). 1
Ramban #2: They were before the Torah was given. We must say that the chiefs ruled simultaneously, each one over his own country, 2 or they all ruled (one after the other) for a very short time. Hashem shortens the life of Resha'im (Mishlei 10:27)!
Ramban: This is unreasonable. Why should the Torah list these? Until what time does it list (surely there were more chiefs after these!
If the chiefs ruled one a time, like kings, like the Ramban initially said, it is difficult to say that 19 reigns finished within 240 years (even less - surely it took years for Edom to conquer Se'ir and establish their first king - PF)!
