Why does the Torah not tell us the name of the king of Edom, like it did with regard to the two kings of the Emori (Sichon and Og)?
Ramban: Because the Torah only mentions the names of those kings that are renowned for their might, to enable us to thank Hashem for His miracles in allowing us to conquer them. 1
Why did Moshe insert the word "Achicha"?
And why did he refer to the hardships that Yisrael endured?
Rashi: To remind Edom that their grandfather Eisav had deliberately moved away, in order to avoid having to fulfill the necessary prerequisite of exile, before becoming a nation, placing the burden fairly and squarely upon the shoulders of Ya'akov.