All you're missing is the metadata of 'name, date of birth, social security number' and so on. But that's just a system we've placed on top of 'who you are', which is your genes.
Your fingerprint, your retina scan, your full lifes history, nothing in that list will identify you as good as your DNA does.
So once you have someones DNA you can reconnect it with the rest of the information at any point in the future by simply checking to see where that DNA turns up again, including fractions of it in your descendants.
You can't really anonymize it.