Your private key information will not be shared to anyone from the wallet providers. If you share by your own and sharing wallet.dat will be hackable by the any people. Bitcoin transaction are anoymous anytime because private information will not share whenever you transferring the bitcoin to any concern wallets. Exchangers will comes to know your bank details when you exchange your bitcoin to fiat cash. I have many time trading but none of the people will not looking into share it anyone.

Yes, we already know that in Bitcoin there is no such thing as absolute privacy. Somewhere along the way, the privacy chain can be broken and the transactions can easily be mined and analyzed. As in anything in life, there would always be exemptions to the general rule. Generally, it should be be anonymous maybe if all things are kept in the Bitcoin network in the sense that any transaction may not have your personal identity imprinted on them (however the details of the transactions are there for the public to see) but when the transaction can be involving third-parties then that is why when things can really be so different.

We are living in a connected and wired world where privacy can be shared for all to record, mine, analyze and utilized. Private data can in fact be a billion-dollar business as there are many commercial entities who are interested to get hold of the data for their own business exploitation. One of the reasons why we have cryptocurrency is to precisely limit the encroachment of these data coming from the government and business industry. But as in anything in life, we could not live alone by ourselves so somewhere somehow we have to compromise to also get what we want.

Everyone can create an wallet in a snap of course without giving any identity also.

And the transaction is secure, encrypted and whatever, BUT are your wallet truly anonymous?

It has a private password and that’s ok when you keep all the BTC in there . I mean IN and OUT.
But when you want to change your BTC with other CCs that’s where you can get pubblic. On the exchange and in many other ways.

Just keep it in mind

It can be very anonymous depending how you cashout your BTC.

If you're only holding BTC and not cashing out for fiat, it can remain anonymous. The moment you cashout using any online method such as PayPal, bank transfer, Skrill etc you can be tracked

Now if you want to cashout anonymously the only way I can think of is face to face without involving any banks etc just trading BTC for cash in hand.