The deep rift between God and the Israelites reaches a devastating peak through the symbolic naming of a child, representing a total severing of their relationship. The name given to the newborn serves as a declaration that the child is not considered the prophet's own son. This harsh reality indirectly cuts off the connection with the mother as well, serving as proof that she bore her children through unfaithfulness [מלבי״ם].
The overarching message that the Israelites are no longer recognized as God's people stems from their own actions. They have stopped behaving like a nation loyal to its sovereign. Instead of carefully following God's words the way a proper nation respects and obeys its king, they have abandoned their responsibilities [מצודת דוד].
As a direct result of this lost loyalty, God responds in kind, withdrawing His presence. On an immediate level, this means He will no longer act as their God and will not stand by their side to rescue them from trouble [מצודת דוד, ביאור שטיינזלץ]. On a deeper level, this separation mirrors a ruined family dynamic. God refuses to continue acting as a father or husband to the people. It symbolizes a formal divorce from the nation, carrying the severe threat that God might replace the Israelites with another people entirely [מלבי״ם].