Answer
In the Old Testament, "Yahweh" is God's name, meaning that it is the name of the Trinity. In the New Testament, God is revealed as existing in Trinity, and both the Father and the Son are at times called "Lord" in passages which quote Old Testament uses of "Yahweh." The Holy Spirit is also called the "Spirit of the Lord" where "Lord" translates "Yahweh" (e.g., Luke 4:18), though as an Old Testament passage it probably should not be understood as speaking directly to Trinitarian doctrine. Still, Paul does say that the Lord is the Spirit (1 Cor. 3:17).
I would say that it is legitimate to call any person of the Trinity "Yahweh," although this probably would not communicate much in most settings. Usually, it is probably more helpful to call Jesus "Jesus," the Father "Father," etc.
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.