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 GP model.
For hospital treatment, there is only very limited capacity to comply to patients' wishes as to the doctor performing their treatment except for doctors with hospital affiliation or holders of supplementary hospital insurance (private oder semi-private). The financial and organisational efforts would be too large. However, all patients may refuse to be treated by a certain doctor.
Here you can find an overview of doctors in your place of residence.