We've taken to calling this style of chip Paranoid, and that's probably a fine thing to continue doing, but recently we've learned more about the history of these kinds of chips such that in some cases "Paranoid" is perhaps not strictly speaking correct.
Paranoid is the brand name that USPCC used for the material that some of their chips were made out of. It's almost certainly a blend of plastic (probably celluloid) and other stuff, including clay. USPCC made at least two different lines of Paranoid chips - Paranoid Inlaid (with symbols, numbers, and letters) and Paranoid Engraved (with various line-drawing designs, including the chips in my avatar picture).
The inlaid symbol chips are what we're usually talking about when we say Paranoid nowadays, because they're ubiquitous and distinctive. They're compression-molded clay chips (Paranoid is the same type of material that we nowadays would call "clay"). They're made using die-cut inlays: a big sheet of colored thin plastic had the symbols cut out of them with a stamp (a "die"), then the symbols were placed on top of the blank clay slug inside the press. The press pressed the symbols into the surface of the chip while heating the chip to cure and set the plastic.
Here's a picture showing what the die-cut inlays look like relative to the chips they were used in:
Now, here's where it gets fun. In the 1940s, Burt Co purchased chip-making equipment from USPCC, including the dies that they used to cut out the symbols for their Paranoid Inlaid line of chips. After that, Burt Co continued making inlaid symbol chips using the USPCC dies (and thus the same USPCC symbols)
BUT they made the chips using their own molds, presses, and clay formulas. And at some point, those molds and formulas were no longer the same as what USPCC had used in earlier days.
So, some time after the purchase, we had symbol chips that looked like the old USPCC Paranoid chips, but were made like Burt chips. Which means they weren't made from the same material, which was called Paranoid.
So.
Technically the chips you just bought aren't "Paranoid" because they aren't made from the same material that USPCC called by that name. I'm pretty sure that these are Burt chips because they're square-edged and thick. BUT we've been calling this kind of inlaid symbol chip "Paranoid" for a long time, and perhaps it's not really a mistake to keep doing so.
Anyway, I think they're pretty cool chips. Good luck finding more with the same design! You'll probably need a good bit of diligence and patience.
This thread summarizes most of what we know about these chips; well worth reading if you liked them enough to buy the lot on
eBay.