Bitcoin was widely touted early on as anonymous – on the blockchain, nobody knows you’re a dog. Of course, with every confirmed transaction logged in the blockchain forever, it’s pseudonymous at best; as the case of Ross Ulbricht and the Silk Road showed , law enforcement will happily do the tedious legwork of tracing your transactions if you motivate them sufficiently.
There are ways to increase your anonymity, such as mixers – send coins to an address, they shuffle them with other people’s coins, and you get them back later minus a percentage. (Assuming the mixer isn’t a scam that just takes your coins.) There is also the trick of buying a chain of other cryptocurrencies in succession, to cloud your trail over multiple chains; though exchanges are increasingly wise to this one and tend to kick such traders off for obvious money laundering.