Yes and no. Blockchains are all publicly visible. Everything that happens on them is public knowledge. Rather than anonymous, though, they are psuedo-nonumous. That is to say, any knowledge of somebody’s identify is contextual. If you can confirm, with certainty. that somebody owns a given wallet address you can then start tracing what they’re doing. For example, you can know who somebody is based on them publicly posting about owning a given NFT. That contextual information ties them to the wallet and all the transactions attached to it and now everything you do on the blockchain is, effectively, public knowledge unlike with traditional finance where there are strict laws in place to (mostly) protect your privacy. While not perfect they do (mostly) work.
Source for that last bit is that I used to be a software developer for a major financial institution in my country and had to deal with privacy matters from time to time.
Edit: spelling mistakes