That the trickle-down theory of economics has enjoyed such marketshare in the public mind for the last thirty odd years is testimony to the power of branding. Similar names for the same product, "supply-side economics" and "voodoo economics" have been less successful. "Supply-side" is still used because although only a few economists actually know why it's called that, you can sound like you know what you're talking about. "Voodoo economics" doesn't afford that cover; if enough people claim to understand something, then calling it inexplicable nonsense will backfire by making them look smarter for understanding it, whether they actually do or not.
The real strength of the trickle-down metaphor is in its simple and obvious intuitive imagery. Of course water trickles down from wherever you pour it, eventually finding its way to the bottom. It's a law of nature, this gravity thing, and pretty widely accepted even among Young Earth Creationists (mostly).
The trouble with the metaphor, and with the theory generally, is that it actually mixes two incompatible metaphors, effectively flipping the force of gravity upside down. We call it "trickle-down" because we have a strong tendency to speak of wealth and social class in vertical terms: we have upper and lower classes, prosperous people are upwardly mobile, it's lonely at the top. We accept this social heirarchy metaphor unquestioningly, and in the context of describing social heirarchy, it's just fine. But metaphors are dangerous if we take them too literally, and it's a mistake to assume that the force of gravity in our social metaphor which will bring the high and mighty crashing down into poverty if they're not careful also applies to their money flowing downhill, because that's not what the original metaphor was crafted to explore.
It is useful to think of money as a kind of fluid. We talk of cash flow, liquid assets, currency and charges. But which way does it flow? That's much more complex, because money flows in so many different directions; I might pay you today to do something for me, and you might turn around and use that money to buy something from me tomorrow. In general, though, it's a safe bet that if money is accumulating in any particular place, there's a reason for it: money tends to flow towards rather than away from such places. The mere fact that it's accumulating there is at least prima facie evidence of that.
We generally call people who accumulate money "rich". There are all sorts of reasons why rich people become rich, some of them good, some of them bad. Some people become rich by being really good at providing something that everyone needs. Others are good at gaming the system. Others inherit wealth, others steal it. If you've heard anything about Thomas Piketty's tome, Capital in the 21st Century, you might be aware of his analysis that income from capital tends to be more than growth, which means that wealth will naturally tend over time to accumulate in the hands of those who own capital. But whatever the reason, we can think of these places where money accumulates, regardless of the reason, as "down" with respect to the natural flow of money. Money flows downhill, into the pockets of those who are good at making it, and away from those who are bad at keeping it.
In other words, money does trickle down, but down is where the wealthy are, while the poor live in the arid highlands, praying for rain.