Bitcoins are pseudonymous only. The entire bitcoin ledger is public.
Under the ideal usage of Bitcoin (with Tor, mixed coins etc), you could basically say that you own an "anonymous BTC". The ledger may be public, but if you've been under an anonymous identity the entire time then it's useless really. But a very little mistake could cost your entire effort of protecting your identity revealing everything, of course. 
It's not really anonymous, chain analysis know it's originated from mixer service and they usually call it "tainted BTC". If you use privacy-orianted cryptocurrency such as Monero, chain analysis can't even know the origin of the coin.