"God the Son" is generally agreed to be Jesus.
Do reformed theologians agree that "God the Father" is Jehovah, or is this only something claimed by the denomination calling themselves Jehovah's Witnesses?
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Jehovah is an English rendition of the proper name of God from the Hebrew Bible, also rendered "Yahweh" or YHWH, which means I AM and is referred to as "The Tetragrammaton". It isn't specific to Jehovah's Witnesses, and can be found in many older English translations of the Bible.
In the Hebrew Bible (Old Testament) the doctrine of the Trinity isn't really formulated (Jews would say it isn't there at all) so there is no concept that the name for "God" applies to only one person of the Trinity. It is usually thought that the name(s) refer to "God as a whole".
Jesus in fact equates himself with Yahweh (Jehovah) when he says "Before Abraham was, I AM" (John 8:58).
Reformed theologians regularly use the name "Jehovah" (or its equivalent, "Yahweh"), but they do not limit the name to God the Father: they believe it refers to the Godhead, that is, it is also the name of Jesus and the Holy Spirit.
Isaiah prophesies, that “the Lord of Hosts” shall be “for a stone of stumbling, and for a rock of offence,” (Isa. 8:14). Paul asserts that this prophecy was fulfilled in Christ (Rom. 9:33), and, therefore, declares that Christ is that Lord of Hosts. In like manner, he says in another passage, “We shall all stand before the Judgment-seat of Christ. For it is written, As I live, saith the Lord, every knee shall bow to me, and every tongue shall confess to God.” Since in Isaiah God predicts this of himself (Isa. 45:23), and Christ exhibits the reality fulfilled in himself, it follows that he is the very God, whose glory cannot be given to another. (3.14.11)
Again, the prayer of faith is addressed to him—prayer, which specially belongs to the divine majesty, if anything so belongs. For the Prophet Joel says, “And it shall come to pass, that whosoever shall call on the name of the Lord (Jehovah) shall be delivered” (Joel 2:32). And another says, “The name of the Lord (Jehovah) is a strong tower; the righteous runneth into it and is safe,” (Prov. 18:10). But the name of Christ is invoked for salvation, and therefore it follows that he is Jehovah. (3.14.13)
Regarding the Holy Spirit being Jehovah, Calvin continues:
And when Isaiah had introduced the Lord of Hosts as speaking, Paul says, it was the Holy Spirit that spoke (Acts 28:25, 26). Nay, words uniformly said by the prophets to have been spoken by the Lord of Hosts, are by Christ and his apostles ascribed to the Holy Spirit. Hence it follows that the Spirit is the true Jehovah who dictated the prophecies. (3.14.15)
John Frame, in his Systematic Theology, finds the same connections:
[The NT writers] clearly equate the lordship of Jesus to that of Yahweh. Frequently they cite OT passages that speak of Yahweh and refer those to Jesus. (p451)
As with Jesus, there are many places where NT writers refer to OT texts dealing with Yahweh and apply them to the Holy Spirit. (p471)