Even after Uriah's death, Bathsheba was still referred to as Uriah's wife (2 Samuel 12:9; see also Matthew 1:6). Only here is she called David's wife.
Solomon: In Hebrew, Solomon’s name is pronounced Shelomoh. It likely means “his peace,” from the Hebrew word shalom (peace).
The name may also mean “his replacement.” This meaning comes from the Hebrew root shelem, which can mean “replacement” or “compensation.” Similar names include Shelemiah (Jeremiah 36:14), which means “Yahweh has provided compensation,” and Shelumiel (Numbers 1:6), which means “God is my compensation.” Both meanings fit the context of Solomon’s birth after the loss of David and Bathsheba’s first child.