From my understanding, cryptos enable you to do anonymous transactions by hiding your IP during those transactions. However, you're still able to give information about yourself when you're making a payment with crypto for example. Otherwise how could the company who receives the payment check your identity? Then what's behind the concept of "anonymous"?
I think it depends on the cryptocurreny and the service you will use. if you use services like exchange of course they can trace you because almost all exchanges require all its users to provide their identity so if you dont want to be traced dont use exchanges but it will be hard for you to convert your coins to real money. it also depends on the coin because their are cryptocurreny that can be trace like bitcoin but there are some that is untraceable like monero.