No, they're not going to Bitcoin miners. Ethereum miners, sure.
Etherium fits the bill: it's a digital (bit) currency (coin).
The generic word will be whatever John Q. Public with zero knowledge or care calls it.
The "noobs" will always outnumber the knowledgeable in-crowd. They are the ones who will—ahem—coin the generic term.
You can't say that Bitcoin is responsible in a discussion about GPU shortages. It's flat-out wrong and obfuscates the actual problem. It's Ethereum that's mostly responsible for said shortage, and seeing as how Ethereum is moving to proof of stake soon that problem might be alleviated. Bitcoin uses all custom hardware for mining and is not affecting the GPU shortage. The problem with Bitcoin mining is power consumption, not chip contention.