This has no impact on anything really at all. It’s just re branding, hopefully to clarify things. ETH does not change with ETH2. It’s just a series of upgrades to eliminate wasteful proof-of-work mining and improve scalability.
No, it's something like a train changing tracks: the cargo (ETH 'coins' and other parts of its ecosystem) just moves onto the new tracks. The cargo isn't thrown out, it's not incompatible with the new tracks.
Not a great analogy imho. The ETH consensus change from PoW to PoS changes the way that blocks are signed and validated. No more PoW. Instead, now validators decide. It’s more like unanimous voting. If you try to sign a fake block, you lose some or all of your deposit.