What you're looking for is not IPv6 NAT, that would be pointless and would actually limit your full use of the internet. What you're looking for is Privacy Extensions (https://tools.ietf.org/html/rfc4941). That is done on the OS level and most big operating systems support that. Many have it on by default.
Essentially it means that your OS will change it's internal IP address every so often (every 24 hours?) so any outside observer can't track to see if it's the same machine or a different one. As an end user you don't notice this at all, just like you don't notice DHCP addressing, it just works.