E.g. with non-kyc bitcoin and joinmarket or 1-2 ecash-‚hops‘. 

They can do what they want. 
My name is not connected to them and not to find in their database or on their clientlist. 

Surely there are some more steps needed to be fully private in most cases but the most important thing imo is to buy kyc free and then coinjoin. 

 So assuming they follow everything they can trace, what remains can raise suspicion in just the same way. Also, the elephant in the room is that none of this scales if you want to benefit from large amount of coin.