Genesis 16:13

‘And she called the name of Yahweh Who spoke to her, “You are El Roi (‘the God Who sees')”, for she said, “Have I even here looked after Him Who sees me?” '

She gives God a new name as being her personal God, for He has seen her need and has responded. She knows that she has met the One Who sees her always. These words emphasise how dramatic her experience has been. She knows she has experienced a theophany. From now on she is not only within Yahweh's covenant with Abram, she also has her own personal covenant. Yet that personal covenant is within the greater covenant and acknowledged by Abram.

“Looked after” i.e. followed with her eyes. The suggestion is that she saw a partial revelation of Yahweh other than just the appearance of the angel of Yahweh in human form (compare Judges 13:20; Exodus 33:17).