Bitcoin is pseudonymous. Not completely anonymous. Your wallet addresses are stored on a publicly accessible ledger, or blockchain. So your bitcoin address is recorded. Your identity is not, so it stays private. However, funding an account, or withdrawing from an account, is getting harder to do competely anonymously, as countries and businesses feel it’s in their best interest to know who they are dealing with. So KYC (know your customer) regulations, the requirement to give up personal information about yourself, are ever increasing.
Also, exchanges and crypto related business, if in a country that values financial law and financial protections, often keep network/IP transaction history, often tied to wallet addresses. I imagine that those organizations with the correct amount of legal authorization could “persuade” these businesses to give up relevant personal customer information if the need was great enough.
So unless you were concealing your network connections, and then moving your funds around between different wallets and maybe even mixers/tumblers, being completely anonymous isn’t so easy. Laws and regulations are also changing that may make complete anonymity impossible (depending on where you live).