The name of the mountain where the Edomites resided. Originally, the Horites lived here.
It can be seen that the name of the person who originally lived in this area was Seir, and as his descendants resided there, it became the name of the region.
Gen 36:20These are the sons of Seir the Horite, who were living in the land: Lotan, Shobal), Zibeon, Anah),Gen 36:21Dishon, Ezer), and Dishan. These were the chiefs of the Horites, the sons of Seir in the land of Edom.
Deut 2:12(Horites also lived in Seir formerly, but the descendants of Esau dispossessed them and destroyed them from before them and settled in their place, just as Israel did to the land of their possession, which the Lord gave to them.)
Esau later conquered it and made it his dwelling place. God did not allow the Israelites to invade Edom during the Exodus.
Deut 2:2And the Lord said to me,Deut 2:3‘You have been circling this mountain country long enough. Turn northward.Deut 2:4And command the people, “You are about to pass through the territory of your relatives the descendants of Esau, who live in Seir; and they will be afraid of you. So be very careful.Deut 2:5Do not contend with them, for I will not give you any of their land, not even a foot’s length, because I have given Mount Seir to Esau as a possession.Deut 2:6You shall purchase food from them with money, that you may eat, and you shall also buy water from them with money, that you may drink.”Deut 2:7For the Lord your God has blessed you in all the work of your hands. He knows your journey through this great wilderness. These forty years the Lord your God has been with you; you have lacked nothing.’
It was later conquered during the time of David.
2 Sam 8:13And David made a name for himself when he returned from striking down 18,000 Edomites in the Valley of Salt.2 Sam 8:14He also put garrisons in Edom; throughout all Edom he put garrisons, and all the Edomites became David’s servants. And the Lord gave victory to David wherever he went.