Since יהוה or "He who is" (the name which St. Thomas Aquinas, the 'Angelic Teacher' of the Church, arrives at by logic as the only apt name for the kind of Creator we must needs acknowledge as responsible for creation) can only refer to the Eternal Creator, it must mean the Divine Nature and as such can be used of the Father, the Son, or the Holy Ghost equally.
Since the Fourth Lateran Council states:
Fourth Lateran Council, Canon 2.
...there is one supreme entity, incomprehensible and ineffable, which is truly Father, Son, and Holy Ghost, together (simul) three persons and each one of them singly. And thus in God there is only trinity, not quaternity,1 because each of the three persons is that entity, namely, substance, essense, or divine nature, which alone is the principle of the universe and besides which there is no other.
thus the Father and Son as well as the Holy Ghost proceeding from both are the same entity.
Without question "divine nature," "one supreme entity...alone the principle of the universe" etc. corresponds to "the one who is" (יהוה) and thus all three Persons are equally and rightly called יהוה.
As far as early Church Fathers go, they variously interpret certain passages where God (יהוה) speaks to be either the Father or the Son or Holy Ghost. A good example is this passage from St. Justin:
Justin Martyr, First Apology, 37-39
And that this too may be clear to you, there were spoken from the person of the Father through Isaiah the Prophet, the following words: "The ox knows his owner, and the ass his master's crib; but Israel does not know, and My people has not understood. Woe, sinful nation, a people full of sins, a wicked seed, children that are transgressors, you have forsaken the Lord." And again elsewhere, when the same prophet speaks in like manner from the person of the Father, "What is the house that you will build for Me? Says the Lord. The heaven is My throne, and the earth is My footstool." Isaiah 66:1 And again, in another place, "Your new moons and your sabbaths My soul hates; and the great day of the fast and of ceasing from labour I cannot away with; nor, if you come to be seen of Me, will I hear you: your hands are full of blood; and if you bring fine flour, incense, it is abomination unto Me: the fat of lambs and the blood of bulls I do not desire. For who has required this at your hands? But loose every bond of wickedness, tear asunder the tight knots of violent contracts, cover the houseless and naked, deal your bread to the hungry." Isaiah 1:14, Isaiah 58:6 What kind of things are taught through the prophets from [the person of] God, you can now perceive.
And when the Spirit of prophecy speaks from the person of Christ, the utterances are of this sort: "I have spread out My hands to a disobedient and gainsaying people, to those who walk in a way that is not good." Isaiah 65:2 And again: "I gave My back to the scourges, and My cheeks to the buffetings; I turned not away My face from the shame of spittings; and the Lord was My helper: therefore was I not confounded: but I set My face as a firm rock; and I knew that I should not be ashamed, for He is near that justifies Me." Isaiah 50:6 And again, when He says, "They cast lots upon My vesture, and pierced My hands and My feet. And I lay down and slept, and rose again, because the Lord sustained Me." And again, when He says, "They spoke with their lips, they wagged the head, saying, Let Him deliver Himself." And that all these things happened to Christ at the hands of the Jews, you can ascertain. For when He was crucified, they did shoot out the lip, and wagged their heads, saying, "Let Him who raised the dead save Himself." Matthew 27:39
And when the Spirit of prophecy speaks as predicting things that are to come to pass, He speaks in this way: "For out of Zion shall go forth the law, and the word of the Lord from Jerusalem. And He shall judge among the nations, and shall rebuke many people; and they shall beat their swords into ploughshares, and their spears into pruning-hooks: nation shall not lift up sword against nation, neither shall they learn war any more." Isaiah 2:3 And that it did so come to pass, we can convince you. For from Jerusalem there went out into the world, men, twelve in number, and these illiterate, of no ability in speaking: but by the power of God they proclaimed to every race of men that they were sent by Christ to teach to all the word of God; and we who formerly used to murder one another do not only now refrain from making war upon our enemies, but also, that we may not lie nor deceive our examiners, willingly die confessing Christ. For that saying, "The tongue has sworn but the mind is unsworn," might be imitated by us in this matter. But if the soldiers enrolled by you, and who have taken the military oath, prefer their allegiance to their own life, and parents, and country, and all kindred, though you can offer them nothing incorruptible, it were verily ridiculous if we, who earnestly long for incorruption, should not endure all things, in order to obtain what we desire from Him who is able to grant it.
1 In context, this is against the heretical notion that the Father (actually, and not only as a matter of speaking) 'has' the Divine Nature, which is then made 'other'—that there is Father, Son and Holy Ghost, which 'have' a fourth Thing, the Divine Nature.' No heretic actually worshiped a quadrinity, but the Council rightly rejected this as the obvious conclusion of the heretical understanding of the relationship between the Divine Nature and what it means that the Persons are that Nature.