Traditionally, the divine name (YHWH aka "Jehovah") is associated with God the Father - the God of the Old Testament. Jesus is associated with God the Son, the incarnation of the Godhead.
Traditionally, the LDS answer is very straight-forward: God the Father is one distinct person, Jesus is another. From a non-Trinitarian perspective this is very easy to understand. The problem is, it would seem to violate the notion that "Behold, the Lord your God is One" to Trinitarians. Understand, the Trinity is itself a paradox, but it is the best formulation we have.
In the classic formulation of the Trinity, God the Father ("YHWH") and God the Son (Jesus) are one essence but different persons. As the Athansian Creed puts it:
... we worship one God in Trinity, and Trinity in Unity; Neither confounding the Persons; nor dividing the Essence. For there is one Person of the Father; another of the Son; and another of the Holy Ghost.
The idea is that God is One Essence so throughly in agreement that it is impossible to distinguish their "Godness" from one another. That said, to deny that they have distinct personhood violates scripture that indicates the Godhead is composed of distinctly willed individuals. The Person of God the Father was the Person who gave his divine Jehovah name "I am that I am." The Person of Jesus, who was the incarnation of God the Son is a different person, but indistinguishable in essence from him.
Clear as mud right?
Traditionally, the answer is that the title adheres to God the Father, but in essence, you wouldn't really be able to distinguish them.