If you buy from an exchange with KYC, none of your accounts are private. As soon as you transfer your coins from the exchange into your wallet, your wallet address is linked to your name. Then any other account you transfer to from your wallet can be figured out as your other wallets.
If you keep your wallet on your phone, the phone company knows who you are so they could track your wallet addresses.
If you buy crypto from a non kyc exchange on your computer your ip could be tracked and since your cable company knows who you are they could see your wallet addresses and know who you are.
If you use a VPN to buy crypto on a non kyc exchange and store it onto a cold wallet your might be safe. Assuming you don’t send coins to someone you know who has been identified or you send to an exchange to cash out.
TLDR: if the government or irs wanted to figure out who’s public addresses where who they could.
Better explanation- https://youtu.be/2OIO5wBoQlQ