"The branding name does matter." That's what I meant when I said it would still be (called) Bitcoin. Nobody asks if they take BTC, they say Bitcoin. Replay protection is anti-bitcoin.
No if BTC changed to SGT people will start calling it Segwit or segwit coin. "Formerly Known as Bitcoin"
Stupid exchanges would be sued for market manipulation and lose they KYC/AML licenses or whatever fiat requires. New exchanges would take their place overnight.