Right now, yes, the LDS church absolutely believes that Jehovah is a name exclusively used for Jesus Christ in the Old Testament. This answer will be long though because of how the LDS church's view of revelation effects what is canon in our religion.
Essentially what we believe comes from God to the prophets and apostles and stays there until a later Prophet revokes that belief on behalf of God. Meaning our beliefs essentially are reinforced or discarded every time an apostle or prophet speaks and every time one of them speaks officially for God it is published publicly for everyone to see. Luckily this topic has been covered multiple times in favor of Jehovah as being the correct name for Jesus Christ in the OT, unless of course it was mistranslated.
And recently in 2018, this belief out is explicitly stated by Russel M. Nelson the current Prophet. (Considering how he is talking about the importance of names in this sermon and specifically points this out I find it hard for this to not be verifiable.)
October 2018 General Conference, "The Correct Name of the Church"
"...What’s in a name or, in this case, a nickname? When it comes to nicknames of the Church, such as the “LDS Church,” the “Mormon Church,” or the “Church of the Latter-day Saints,” the most important thing in those names is the absence of the Savior’s name. To remove the Lord’s name from the Lord’s Church is a major victory for Satan. When we discard the Savior’s name, we are subtly disregarding all that Jesus Christ did for us—even His Atonement.
Consider this from His perspective: Premortally, He was Jehovah, God of the Old Testament. Under the direction of His Father, He was the Creator of this and other worlds. He chose to submit to the will of His Father and do something for all of God’s children that no one else could do! Condescending to come to earth as the Only Begotten of the Father in the flesh, He was brutally reviled, mocked, spit upon, and scourged. In the Garden of Gethsemane, our Savior took upon Himself every pain, every sin, and all of the anguish and suffering ever experienced by you and me and by everyone who has ever lived or will ever live. Under the weight of that excruciating burden, He bled from every pore. All of this suffering was intensified as He was cruelly crucified on Calvary’s cross..."
Also, one sure-fire way to verify this (You would think.) is that this is a canon belief is that it is stapled to the back of our bible in the Bible Dictionary.*
"...Jehovah is the premortal Jesus Christ and came to earth being born of Mary (see Mosiah 3:8; 15:1; 3 Ne. 15:1–5; D&C 110:1–10). Although Ex. 6:3 states that the God of Israel was not known by the name Jehovah before Moses’ time, latter-day revelation tells us otherwise; see JST Ex. 6:3 (Ex. 6:3 note c); Abr. 1:16; 2:8; see also Gen. 22:14."
*Unfortunately it has this disclaimer. "...This dictionary is provided to help your study of the scriptures and is not intended as an official statement of Church doctrine or an endorsement of the historical and cultural views set forth."
Another example of this is the Guide to the Scriptures to the scriptures on our website which has a similar disclaimer.
"See also I AM; Jesus Christ
The covenant or proper name of the God of Israel. It denotes “the eternal I AM” (Ex. 3:14; John 8:58). Jehovah is the premortal Jesus Christ and came to earth as a son of Mary (Mosiah 3:8; 15:1; 3 Ne. 15:1–5). Usually, when the word Lord appears in the Old Testament, it means “Jehovah.”
JEHOVAH IS CHRIST
Jehovah was known to the ancient prophets (Ex. 6:3; Abr. 1:16). The Apostle Paul taught that Christ was the Jehovah of the Old Testament (Ex. 17:6; 1 Cor. 10:1–4). The brother of Jared in the Book of Mormon saw the premortal Christ and worshiped Him (Ether 3:13–15). Moroni also called Christ “Jehovah” (Moro. 10:34). At the Kirtland Temple, Joseph Smith and Oliver Cowdery saw the resurrected Jehovah (D&C 110:3–4)."
Also, The Brother of Jared in THe Book of Mormon meets God who reveals himself to be Jesus Christ before he is born in spirit form in the book of Ether although he does not specifically call him Jehovah. Ether 3:14 (Keep in mind The brother of Jared is THE brother of THE Jared from the OT during the period just after the tower bable.)