The cost of out-patient treatment in the vicinity of your workplace or home is covered by basic insurance. Patients are free to choose their doctor unless they have the HMO or family doctor model.
In hospital, patients can rarely choose their treating physician, unless they are in a hospital with attending doctors or holders of supplemental hospital insurance (private oder semi-private). The expenses in terms of human resources and the organisational effort would be too great. However, patients may refuse to be treated by a physician they do not like.
Here you can find a list of doctors working in your region.