‘And YHWH said, “Call his name Lo-ammi, for you are not my people, and I will not be your Ehyeh (I AM).”
The message proclaimed by the naming of this child would come as a profound shock to those who took notice, mainly the faithful in Israel. Whereas the first two names had been somewhat ambiguous, the first affecting the royal dynasty and the national security, and the second reflecting a certain coldness in their relationship with YHWH, there could be no doubt about what this one signified. It was Lo-ammi' and indicated ‘not My people'. It was notification of the direct rejection of Israel as YHWH's people.
Furthermore He would no longer be their Ehyeh (‘I am' or ‘I will be'). Ehyeh was the name of God stressed when God came to Moses prior to the Exodus (Exodus 3:14). The idea is that God will no longer be acting on their behalf. From now on they could not look to Him for deliverance. Exodus 6:7 (‘I will take you for My people, and I will be your God') is to be seen as having been reversed. This was because the kind of religious exercise in which they now indulged in the name of YHWH was looked on as meaningless, having become prostituted to the level of a nature religion. They no longer saw YHWH as the covenant God of Sinai, the Deliverer from Egypt, but simply as a parallel to Baal.