You're making alot of assumptions
It's unlikely that people will choose to transact on the S2x chain, Bitpay and Coinbase aren't enough to keep it going, alternative to both have existed for years.
And the "who's calling what an altcoin" stuff is a pretty funny joke. It doesn't matter what's called what, it's about the overall technology model behind the coin that counts. Being called "Bitcoin" isn't a magic trick that makes something valuable money, unfortunately
I have been trying to clearly outline my assumptions so that they can be challenged.
For instance
Comments assume the miner/exchange cohesion continues. (still applies)
Other Assumptions:
that the supporting exchanges will follow their stated position to follow the majority hash power.
defining a new core hash for POW, testing of it, deploying it and achieving significant usage will take finite, non-trivial, time.
a large fraction of bitcoin users are not super-knowledgeable about crypto currency algorithms
a large fraction of users get their bitcoins from majority hash following exchanges and not peer-to-peer at least for the next year.
a large fraction of users who spend their bitcoins with merchants do so by way of merchant support from companies like Bitpay.
I am willing to update/revise my assumptions based on discussion if appropriate. I sure don't think I have all/most/many of the answers. On the other hand I don't think my assumptions are far off. The most interesting one, in my opinion, is miner cohesion but I don't speak Chinese so I can't help there.
Coinbase, Bitpay, Gemini, and quite a large number of heavy hitters are spelled out in the New York Agreement.
relative to "who's calling what an alt coin" It aint me babe. Its (assuming miner/exchange cohesion continues) Coinbase, Gemini, Bitpay and on and on that have tons of real customers who will be calling Bitcoin-from-segwit2x Bitcoin/BTC and to use their services a Core supported coin won't be that. It will be like eth or ripple or bitcoin cash - AN ALTCOIN.
One actually needs some assumptions defined if you want to attempt to reasonably model the future progress of something