A discussion on the relationship between two of the most important names of God:
The OT begins with reference to Elohim rather than Yahweh (Gen 1:1); this may indicate that it more readily carried a universal sense for that audience than the personal name Yahweh. The addition of Yahweh to Elohim, ‘Lord God,’ in Gen 2:4-3:23 may be meant to claim that this universal creator God is none other than Israel’s personal God. That the name Yahweh was invoked from earliest times (Gen 4:26), and this by non-Israelites in a setting what has all of humankind in view, may reflect a comparable universal intention related to worship. Yahweh is a God for all people and may be prayed to and worshiped by all (see 1 Kings 8:41-43). The constant interchange between Elohim and Yahweh in subsequent Genesis narratives, particularly with their lively interest in the interaction between the chosen family and the surrounding peoples, may carry this universal intention forward. That this carries a missional interest may be seen in the repeated word that Abraham has been chosen for the sake of ‘all peoples of the earth’ (Gen 12:3 and par.). Election is for mission.
William Van Gemeren, gen. ed., New International Dictionary of Old Testament Theology & Exegesis, vol. 4, 1295.