'That Being (i.e. that which had produced fire, water, and earth) thought, let me now enter those three beings (fire, water, earth) with this living Self (gîva âtmâ), and let me then reveal (develop) names and forms.

In plain words: The father, Uddalaka, tells his son Svetaketu that the one Being, after making fire, water and earth, decided to enter into them as the living Self. Then it would give everything its names and shapes.