Why did Ya'akov name the place 'Beis-El' again?
Peninim mi'Shulchan ha'Gra (Bereishis 28:19), Ha'Kesav veha'Kabalah (Bereishis 28:19): Yakov called three [different] places Beis Kel (Bereishis 28:19), Kel Beis Kel (Bereishis 35:7), and Elokim Beis Kel. 3
I.e. in this verse, 'Elokim' does not refer to the previous words (to teach that Elokim spoke with him), rather, to the coming words (it is part of the name of the place). The Trup supports this.
Why does the Torah repeat the phrase "the location where Hashem spoke with him" a number of times in the Parshah (See, for example, Pasuk 14)?
Rashbam: Because Hashem spoke with him in an open place, and not in a town.