As an earthly king, the Lord Jesus ties together two successions from Scripture. As King of Israel, He succeeds David (2 Samuel 5:3; John 1:49). As King of Kings, He succeeds Nebuchadnezzar (Daniel 2:37; Revelation 17:14; Revelation 19:16). It seems to me that the title "Son of God" corresponds to the first title (John 1:49), while the title "Son of Man" corresponds to the second – it's the Son of Man who is given a kingdom that shall never end (Daniel 7:13–14).
When David announced Solomon as his successor, he had him ride through Jerusalem on a mule (1 Kings 1:32–48). God announced His own Son as David's successor in the same way (Matthew 21:1–16). I'm sure I've mentioned this before, but we see the Lord riding only twice in Scripture: once on a donkey, once on a white horse. And these two scenes correspond to the titles "King of Israel" (Matthew 21:5) and "King of Kings" (Revelation 19:16).
It's easy to forget that God Himself set up Nebuchadnezzar as King of Kings (Daniel 2:37–38; Jeremiah 27:4–8), but it's true. God set up Nebuchadnezzar as king just like He set up David as king (Psalm 78:70–72). By the time we get to Nebuchadnezzar, the Old Testament has detailed how the nation of Israel had fallen into disrepair. It was, indeed, a nation in ruin. So it's easy to see Nebuchadnezzar as a judgment brought on Israel (and he was), but we shouldn't let that overshadow what God was doing with him. The Most High rules in the kingdoms of men, and He gives them to whomever He wills (Daniel 4:31–32).
But the fact is, when we refer to the Lord as "King of Kings," we are using a title He gets from Nebuchadnezzar and the gentile kings (cf Ezra 7:32). It's a title God gives Him, but just like "King of Israel," the Lord is the last, and not the first, to hold it.
So when we read the captivity and post-captivity books of the Bible, we get another glimpse of the Lord as King. It's not the same point of view that we get when we see the lives of the kings of Israel, but it's equally true.
I wouldn't actually say that the Lord will have two kingdoms: but I could be wrong about that. I remain convinced that the New Covenant is exclusively between the Lord, Israel, and Judah (Jeremiah 31:31–34; Hebrews 8:7–11). I don't see that the gentiles have any part in that. The title "King of Kings" is given to both Nebuchadnezzar (Daniel 2:37) and Artaxerxes (Ezra 7:32), but they definitely had two separate kingdoms. So it's not apparent to me that these two kingly titles necessitate two kingdoms: "King of Kings" doesn't seem to be tied to a specific kingdom.