Is Bitcoin really anonymous?
No, most people describe it as pseudonymous.
When people say that, what they mean by Bitcoin is the tools, technology and network described by Satoshi Nakamoto in the original whitepaper where he described a system of electronic cash that did not rely on trusting third parties.
They usually don't mean the parasitic third-party businesses like Kraken that some people trust with their money.
Bitcoin itself can be relatively anonymous even when parasitic businesses choose not to be (or are forced by governments not to be).
If you feel these parasitic third-parties are exposing your identity more than you are comfortable with, don't use them.
Since the beginning of time, security and convenience work against one another. If you value something - privacy say - you have to invest hard work and money in achieving that and you have to sacrifice some or all convenience.
Note that although I characterise third party exchanges as parasitic, this is mainly for rhetorical effect. They are parasitic but many of them do offer valuable services and provide the convenience that many of us seek. I don't think it right to use a more sympathetic adjective like symbiotic because I think the vision offered by Nakamoto was of a system of cash that could thrive without any dependency on trusted third parties.