The relationship of the Father, Son, and Holy Spirit is considerably more mysterious than is implied by the expression “persons of the Trinity.”
The word translated LORD in the King James is always the tetragrammaton YHWH.1 This word is used in combination with other words to emphasize specific qualities of God. Whenever either Jehovah or LORD is used in the King James Bible, it is used in reference to YHWH.
The King James translators translated YHWH as Jehovah Yir’eh, “The LORD provides” (Genesis 22:8,14); YHWH Shalom, “The LORD is peace” (Judges 6:24); YHWH Tsidkenu, “The LORD is our righteousness” (Jeremiah 23:6); YHWH Shammah, “The LORD is there” (Ezekiel 48:35).
When the most commonly used Hebrew word for God, YHWH, was translated into Greek, the word Kurios (Lord) was used. This is the same Greek word used by the followers of Christ to refer to the Savior.
The New Scofield Reference Bible has a helpful comment on this aspect of God’s redemptive name:
Jehovah is distinctly the redemption name of Deity. When sin entered the world and man’s redemption became necessary, it was Jehovah Elohim who sought the sinning ones (Gen. 3:9-13) and clothed them with coats of skins (Gen. 3:21), a beautiful type of the righteousness provided by the LORD God through sacrifice (Rom. 3:21-25). The first distinctive revelation of Himself by His name Jehovah was in connection with the redemption of the covenant people out of Egypt (Ex. 3:13-17).
As Redeemer, emphasis is laid upon those attributes of Jehovah which the sin and salvation of man bring into exercise. These are (a) His holiness (Lev. 11:44,45; 19:1,2; 20:26; Hab. 1:12,13); (b) His hatred and judgment of sin (Deut. 32:35-42; cp. Gen. 6:5-7; Ex. 34:6,7; Ps. 11:4-6; 66:18); and (c) His love for and redemption of sinners, which He always carries out righteously (Gen. 3:21; 8:20,21; Ex. 12:12,13; Lev. 16:2,3; Isa. 53:5,6,10). Salvation by Jehovah apart from sacrifice is unknown in Scripture.
However, we should not limit the use of the name Jehovah to Jesus Christ alone. The Old Testament is not as explicit in the identification of the persons in the Godhead as is the New Testament. There are three primary names for God in the Old Testament but these do not really correspond with the three Persons of the Trinity as revealed in the New Testament. There are some occasions when the name Jehovah might better apply to the Father or the Trinity as a whole.