In Trinitarian orthodoxy,
- יהוה (YHVH), commonly referred to as "the Tetragrammaton," is the name of God.
- The Father is God, and thus, the name of the Father is YHVH.
- The Son is God, and thus, the name of the Son is YHVH.
- The Holy Spirit is God, and thus, the name of the Holy Spirit is YHVH.
- As there is only one God, there is only one name יהוה shared by three persons of the Holy Trinity.
To note, יהיה - no matter what one assumes the nekkudot to be - could not translate into English as "I am." That would be אֶהְיֶה (ehyeh).
My own personal studies leads me to the conclusion that
the Tetragrammaton consists of the name יָהּ (cp. Ps. 68:4), combined with the present participle of the verb הָיָה (hayah), that is, הוֹוֶה (hoveh). Thus, a likely pronunciation may be
Ye-ho'-veh, and the meaning loosely interpreted as "Yah is [the] existing one" or "Yah is [He] who is." When יָהּ is joined to הוֹוֶה, the kamatz nikkud (the phoneme /a/) is subjected to חוק החיטוף ("the rule of hatafing"), which is referred to as "propretonic reduction" by English-speaking Hebrew grammarians. Consequently, the kamatz nikkud becomes a shva nikkud (/e/ phoneme), causing the pronunciation "Yeh-" rather than "Yah-."
And many nations shall be joined to YHVH in that day and shall be My people, and I will dwell in your midst (cp. Zech. 2:10), and you shall know that YHVH of hosts sent Me to you (cp. Zech. 2:9).
Note the two persons identified by the name יהוה. The one who sends is the Father, and the one who is sent to dwell among Israel is the Son. This theme is especially emphasized in the Gospel and Epistles of John (cp. John 1:14; John 8:42; 1 John 4:14).