And he sent messengers to Bilam the son of Beor, to Pesorah, which is by the river of the land of the children of his people, to call him, saying: Behold, a people has come out of Egypt; behold, they cover the eye of the land, and they are settled opposite me.
Torah Temimah: Sanhedrin 105a — R. Yochanan on “son of Beor” versus “his son Beor” (24:3).
English: And elsewhere it says, “the speech of Bilam his son Beor.” R. Yochanan said: He is his father, and he is his son in prophecy.
Resolution of variant name formulas across verses.
Beor is biologically the father; in prophecy the son surpassed the father, so the verse can style the relationship both ways.