panopticon unfortunately there is no solution to your problem.
Let me first re-phrase your problem.
You want to make sure that your carrier does not know your location, while also providing you with the service.
The answer is:
Your carrier must know your location to be able to provide you with the service.
Here when I am saying "location", I am not referring to your phone's "Location" permission.
The towers that provide you with the carrier service can always estimate your approximate location, which you might have heard as "triangulation".
That is simply how carrier services work and there is no other way.