I don't think it's too much of a coincidence.
If we look back at the law for kings in Deuteronomy 17, It prohibits the king from multiplying horses and chariots, wives, and wealth. This is exactly what Solomon is doing in 1 Kings 10-11. Chapter ten begins by commending his great wisdom, but then steps through his decline - that is, he begins violating the rules for kings by multiplying gold (666 talents a year), multiplying horses and chariots, and finally multiplying wives who turn his heart away from following Yahweh. He sets up centers of false worship for all the foreign gods of his wives. So, the number 666 is associated with Solomon in his fall, his abuse of power, and his turning away from true worship of Yahweh.
In Revelation, Jesus sets up worship interactions under the symbol of business transactions - buying and selling.
I counsel you to buy from me gold refined by fire, so that you may be rich, and white garments so that you may clothe yourself and the shame of your nakedness may not be seen, and salve to anoint your eyes, so that you may see.
This is picked up in chapter 13 with reference to worship in the false temple - the image set up by the beast which must be worshiped on pain of death. Everyone must worship the image, but no one may do so without the mark. The buying and selling referred to here is of the same kind established by Jesus in chapter 3. It is worship - spiritual transactions.
This kind of forced worship of an image set up also has ties back to Nebuchadnezzar.
King Nebuchadnezzar made an image of gold, whose height was sixty cubits and its breadth six cubits... And the herald proclaimed aloud, “You are commanded, O peoples, nations, and languages, that when you hear the sound of the horn, pipe, lyre, trigon, harp, bagpipe, and every kind of music, you are to fall down and worship the golden image that King Nebuchadnezzar has set up. And whoever does not fall down and worship shall immediately be cast into a burning fiery furnace.”
Nebuchadnezzar is acting as a beast (and later, even more so) and sets up an image to be worshiped. Again, we have six and sixty associated with worship of a false image on pain of death.
All of this comes together in the name and number of the man - 666. This sums up man in his fallen state. The number carries with it the fallen glory of Solomon, his degraded wisdom, his failure to follow the word of God, his abuse of power, and his allowing himself to be turned aside to the worship of impotent gods.
Don't be afraid of symbolism; it's good for you :)