Pette
https://www.youtube.com/watch?v=HYNZKQZEHoU
There's no perfect 100% private options, but you can do some things to reduce. As far as disassociating your info from your SIM, you can go instore and purchase a sim starter package ( like mint mobile), paid for in cash, register it under an alias and load it with a prepaid gift card.
At that point your service is anonymous, but not private since you're still interacting with cell towers. Mint is probably still logging all your calls and texts and location data. People who want very private phones use VoIP for calls and texts, have no SIM card, and only send and receive calls and texts via WiFi; which is not very realistic for most people.