What name did the LORD send through Nathan for the baby Solomon?

Answer: Jedidiah

The LORD loved the child and sent word through Nathan the prophet to name him Jedidiah because the LORD loved him.

“Then David comforted his wife Bathsheba, and he went to her and lay with her. So she gave birth to a son, and they named him Solomon. Now the LORD loved the child and sent word through Nathan the prophet to name him Jedidiah because the LORD loved him.”— 2 Samuel 12:24-25 (BSB)