The Hebrew text says "the angel of the Lord appeared." The Targum Pseudo-Jonathan on Exodus (3:2) gives that angel a name.
"And Zagnugael, the angel of the Lord, appeared to him in a flame of fire in the midst of the bush. And he gazed, and, behold, the bush burned with fire, yet the bush was neither burned nor consumed with fire."
Zagnugael. The name is unusual — a blend of Aramaic and esoteric angelology — and the Targum is one of the few texts to preserve it. In the tradition, Zagnugael is the angel of divine flame, a herald whose role is to clear the ground for the voice of the Holy One Himself. He is a kind of usher. He burns brightly, but he is not the speaker of the words that will follow.
This is an important Jewish theological point. The fire in the bush is angelic. The words that come out of the fire are God's. The angel precedes the voice but does not replace it. Zagnugael is the stage light; the speaker is the Memra of the Lord.
And the bush itself — ha-seneh. A thornbush. The smallest, spiniest plant in the Sinai wilderness. The Holy One could have chosen a cedar, an oak, a flaming mountain. He chose a shrub. The sages of our <a href='/categories/midrash-aggadah.html'>Midrash Aggadah collection</a> taught that God descended to a thorn to show that no place is too low for His Presence. In slavery, He dwells among the slaves. In a thornbush, He speaks from within the thorns.
Beloved, where you feel smallest, burning, and uncared-for — stand closer. The Memra may be speaking from exactly that bush.