So I've been doing a lot of reading on bitcoin privacy a lot lately, and I've got a question. I'm not sure if this is the right board for this, but I feel it is.
If you are carelessly shared things on Internet, it will be there forever and your privacy lost forever and can not be resumed.
So let's assume an address has been made public and everybody knows who that address belongs to, can the owner decide to change that address and move his coins to another address without it showing on the bitcoin blockchain?
It is impossible because you missed an important point about Bitcoin blockchain. It is a public blockchain, not a private blockchain and all transactions are publicly and traceable by everyone.
This explains why hackers in famous cases will be caught when they moved stolen bitcoin in known addresses to a centralized exchange. Their stolen bitcoin will be frozen by exchange and wait for further action from governments.
If you care about privacy, read many documents on it in
Bitcoin Privacy Guides.