Is Bitcoin entirely anonymous? It’s common for people to say that in reality bitcoin is absolutely anonymous but are not knowledgeable enough to know that is pseudonymous . Bitcoin being pseudonymous rather than the assumed anonymous gives us an understanding that each user has a established public address. So that further tells us theoretically bitcoin address can be traced back using an IP address or an exchange account.
We should be more concerned about to what level or extent is bitcoin anonymous ?
It is pseudonymous.
1) IP address
Bitcoin doesn't work like that. This is one of those things that Satoshi thought about in the design. It's a point of all of the nodes.
A transaction can be initiated through a single command to a node. There are many nodes. It's not impossible to track, but not from the node/bitcoin miner side. A user can also connect and initiate a transfer through any number of IPs, as it doesn't IP restrict transactions.
An address/user can theoretically be tracked by their IP, but it would be very, very difficult to do so. Keeping track of all of the connecting nodes, but not just to your node but to all nodes, is an impossible task. If a person is running a full bitcoin node, then there is a lot of traffic coming in and out, that it is difficult to distinguish what might be their own transactions versus that of other users.
IP isn't a killer tracking mechanism.
2) Exchange account
This requires that a person uses an exchange account. Exchange accounts require KYC, which are often are country information limited. Large transaction amounts to/from cash will require KYC, which, arguably maybe shouldn't be completely anonymous to authorities.
Exchange accounts are not required from an individual to transact with another individual. Or when third-party bitcoin software is used, like those on phones, these don't always require KYC or exchange accounts.
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There are plenty of examples where bitcoin is completely anonymous. No one knows who Satoshi is, for example. So, it has preserved his anonymity. There are plenty of addresses, such as those listed here:
https://bitinfocharts.com/top-100-dormant_9y-bitcoin-addresses.html that are not publicly linked with individuals.