If you are employed and need financial assistance, you receive money from your job centre; if you are only able to work to a limited extent, or if you are retired, you receive money from the social benefits office (Sozialamt). In the same way, you will receive an electronic health card for the statutory health insurance (gesetzliche Krankenversicherung, GKV). You can choose your doctor, as long as this doctor is affiliated with the statutory health insurance.
If you have not yet applied for money from the job centre or social benefits office, then government agencies such as the social benefits office or health office (Gesundheitsamt) will cover your medical care as benefits for asylum seekers.