You have one coin palmed in each hand. Both coins are identical. Only one coin is ever seen by the audience.

You *appear* to toss the *same single* coin back and forth, between your hands.

In reality, each coin never leaves its respective hand.

The “tosses” are mere phony gestures; you just retain the “tossed” coin in one hand, then display the “same” coin in the other hand.

Should you actually *really* toss a coin from one hand, the result would be *two* coins suddenly appearing in the other hand.

What might this feke feint be called, or referred to as?

It sounds like you are just performing a shuttle pass, pretending to toss a coin into the other hand, but retaining it and showing the other coin. Most of the typical shuttle passes are done with the hands close together, so it looks like you are either dropping a coin from finger palm or the tips of the fingers into the other hand, but a toss is just a wider move. Goshman would use a toss motion to vanish a coin, same thing but without a second coin. If he had a second coin, it could be considered a shuttle pass.
Sankey performs a Flying shuttle pass, where he pretends to toss a coin into the other hand, at the same time putting movement on the coin in the other hand to make it look like the same coin was tossed.

Thanks for identifying the name of that move.

In my much younger days, I’d actually come up with it all by myself (didn’t read about it — just sort of stumbled upon it independently, whilst fooling around with a couple of coins).

And “toss” might not have been the best choice of words. The way I did it, both hands approached each other until they were almost cupped together, palm to palm, to simulate the illusory transfer. It was indeed more of a simple (unseen) “drop.”

Even then, I didn’t have the conceit to think I’d actually “invented” something truly original; since it was such a simple and rather obvious thing, I figured it had to already be out there. But, not being widely read in the literature, I had no idea what it might be called.

Now I know. “Shuttle pass.” Thanks!

As mentioned, Sankey’s Flying Shuttle Pass is about the best example of what you initially described here. It gave more movement or animation to the basic move. Think he covered it in his Revolutionary Coin Magic.

Off-the-top-of-my-head thought: what if, after displaying that you suddenly now have two coins (instead of just one), you then secretly stole a third coin, and then did pretty much the same thing — two coins in this hand/fake toss/two coins in that hand — only to eventually reveal that you now have three coins in play?

And then do it yet again, so as to finally end up with four coins in hand?

It would be sort of a coin version of Multiplying Billiard Balls. Surely this too already exists as a published routine somewhere. What’s it called, who's it by, and where might I find it?

Then — assuming the four coins are quarters — for a climax, turn all four into a single silver dollar?

Or, for that matter, into a folded-up dollar bill?

Gerald Deutch used to borrow a quarter, then every time he tossed it from hand to hand it would multiply, until he had several coins. He would then return the quarter and pocket the rest. I believe it is likely in his book, Perverse Magic, or he published it in Apocalypse

My SwayOn Sleight can create the illusion of a coin in each hand when there is only one. SwayOff can create illusion of only one coin when each hand holds one.
Use of Palmer Slip and Palmer Pick can accomplish this also. Each is described in various eBooks.
Twiddle techniques can also accomplish the desired result of concealing the actual number of coins in play
with a very natural passing of a coin from one hand to the other.

SwayOn is the most versatile and similar to Point Transfer except that the hands do not touch at all. (and pre-dates it)
It is a key move of my 3-Fly where your hands never touch each other, and there is no 'back and forth' actions.

Combined with Shuttle Pass type actions, it is powerful tool to support many one-ahead or one-behind ploys.

Regardless, my experience is that you should always have an actual transfer in the sequence to establish or confirm the Pattern.
Then, various methods can be combined for different settings or a repeat audience.