You may want to switch public insurers or move to private insurance. But you may not be able to do this immediately. If you sign up with a Krankenkasse (public insurer), you generally need to stay insured with that same insurer for 12 months.*
There are some exceptions to this rule. If your insurer raises prices through higher Zusatzbeiträge (additional contributions), then you can switch to a different insurer within the first month of the policy taking effect. Read more about that here.
If you move out of Germany permanently, then you can also cancel your insurance membership.
*Previously 18 months (policy updated in January 2021).