To understand Ezekiel 37, we first need to understand that everything in the Bible emanates from Torah, or the writings of Moses, and thus even more specific future prophecies emanate from earlier words, promises, and prophesies. This passage can be interpreted with at least two natures, and certain things are left unclear and anyone's interpretations of them (unless they be inspired by God) are simply their opinion, trying to make sense of something which can be fulfilled in various directions. You see the same kind of relationship in Ezekiel 37 between Judah and Ephraim for example in Genesis 49:10, which says: "And the scepter shall not depart from Judah until Shiloh come." This seems straightforward, as the passage is usually interpreted to mean a Messianic ruler will emerge from Judah.
This then is used in conjunction to the prophecies given to David that his throne will exist forever. But in fact, the scripture has a dual meaning, as the word "Shiloh" means both "the one to whom it rightfully belongs" and it is also a literal place, which is a city in the territory of Ephraim. Therefore this can also mean "when the one to whom it rightfully belongs comes, the scepter will depart from Judah" and someone could interpret that as going into the hands of Ephraim. Nobody looks at things like this, as this can also mean something that is nearly it's opposite, which is "the scepter will never depart from Judah, because the Messiah will come and he will be from Judah" (the way it is normally interpreted). Notice the passage does not say either interpretation.
Back to Ezekiel 37. A king is mentioned named David. This king is not called "the son of David" as people read into it. The David here and "the son of David" being the same is assumed by people using Biblical interpretation principles, but note that it does not actually say that. This David is referred to as "my servant David" which appears in other places in scripture. A Christian might say "this is talking about Jesus" and maybe it is. However, note that in the New Testament, Jesus is never called "David" or "my Servant David" he is called "the son of David" (Matt 1:1 which refers to David being an ancestor of Jesus) and even "the offspring of David" (Revelation 22:16) which is a different meaning, as this comes from the Greek word "genos" which means Jesus is the "literal son" of David, which cannot mean the same thing as "son of David" in Matt 1:1.
So note the following:
Jesus's apostles did not mention Jesus being "the servant David" anywhere in the New Testament (this would seem that it is important to mention at least one time if this were the same person)
Ezekiel 37 does not say "son of David" but instead says "David" whereas in other places different terminology is used.
Note the dualistic tribal manifestation in Genesis 49:10, then ask "what tribe is 'David' from Ezekiel 37 from?" You will then notice, that it does not say, only two tribes are mentioned, which is: Judah and Ephraim.
We are getting to a point already, where this person is probably not Jesus from the points above. However, it could be.
Well, who could this David be? From what I mentioned already, it could be the following separate things:
a) It could be David from the Old Testament being resurrected to reign under a new united kingdom (another user mentioned this) as this chapter also mentions the resurrection of the dead.
b) This could be another future David character who emerges from Judah, from Ephraim, or either.
c) This could be the son of David, which it does not say - however, people generally assume this.
d) This could be all of these interpretations happening at different times. In other words, it could be a, b and c. There is nothing that says a prophecy cannot be fulfilled many times, and many of them are (such as pronouncements of the cursings and blessings in Leviticus 26 happening over and over again.)
I will suggest a radical interpretation, but one that makes sense to me as a possibility. This is that David is not Jesus, but his Father, who will incarnate (take on flesh) at a future time. I say this because of many things, mainly Revelation 22:16 working together with John 3:16. In Revelation 22:16, Jesus is the "root and offspring" of David. Offspring means, Jesus is David's literal son. The only David he could be referring to here is David from Ezekiel 37. The problem is, that John 3:16 says Jesus is the Only Begotten Son of God (Elohim). My interpretation from this is that David = Elohim incarnating in the same manner that the Son incarnated. Thus, there are two Messiahs. The future David would be both a descendant of Ephraim and partially of Judah through the seed of Jesse, and would bring together the kingdoms and create world peace (Ezekiel 37:26). This is an interesting view, which is somewhat different than what people are looking.
In Judaism, they teach there are two Messiahs, but they deny Jesus being either of them. In the New Testament, Jesus is referred to as "the Savior of the world." The Hebrew word for "Savior" is "Mosiah" and one of the two Messiahs in Judaism is the "Mosiah." Judaism teaches the Mosiah will be born through Ephraim, but the Bible does not say this, they are assuming this and then attribute scriptures in a pattern which sometimes makes no sense to either Judah or Ephraim.
It would be interesting if the Father incarnated through Ephraim and began building the kingdom, only to pass it to his son later when he returns in the clouds of heaven. I think that would be like an "ultimate fulfillment" of these scriptures as Jesus says that he does not do anything, but what he sees the Father do.
This is my own view from reading it, and makes sense with the passages. Thus you have the son of David and the offspring of David actually being the son of God, who incarnates as a person named David, who is Ezekiel 37. However, this passage can also be interpreted to mean the things which I mentioned above. Actually, all of those interpretations make somewhat sense. That is why you will not really know until the kingdom is restored to Israel, and the end times events play out.
I actually think that modern Christianity is taking things out of context in various passages, making a good leader who is a great unifier and builder of peace into an evil person, but the actual evil person will sneak onto the scene later and it will be someone that nobody will expect. Hope that helps.