Noob to Bitcoin cash tracking question

Hi there

I would like to buy a VPN service using crypto to stay as anonymous as I can (instead of paying with a credit card and I am directly associated bro the VPN account). Not that I will do something bad but just trying to reduce exposure.

1.- I got the crypto from a centralized exchange like Coinbase, so there is a record of what I purchased. 2.- I moved the crypto to my cold wallet.

My question is if I use my cold wallet to pay for the VPN it is still tracking back that it is me?.

Also, what do you recommend to clean track of transactions if I am purchasing on Coinbase? Or should I use something else?.

Thank you.