Your prefix can change yes but the recommendation is that it shouldn't in practice. You'll find ISPs doing it right will extend your PD lease infinitely unless you release it for a long enough period of time. Similar to ipv4.
The privacy is similar to ipv4 also. All your traffic on ipv4 looks like it's coming from your WAN IP... Your PD is in this sense equivalent (though not literally equivalent for all the pedants reading) to your WAN IP.