Costs for outpatient treatment within the area where you work or live is covered by basic health insurance. Patients may choose their physician, as long as they are not covered by the HMO or family doctor model.
For hospital treatment, there is only very limited capacity to comply to patients' wishes in terms of treating physician, except for physicians with hospital affiliation or holders of supplemental hospital insurance (private oder semi-private). The financial and organisational efforts would be too considerable. However, all patients may refuse to be treated by a certain physician.
Here you can find an overview of physician active in your region.