Every reference lab in the US is required to have a medical director who is legally accountable for quality. That doctor's name will often appear somewhere on the report but that doesn't mean they ordered it. The ordering provider (if any) will be listed on a separate field.

Yes, there is an ordering physician.

The parent commenter we're both responding to said "I can go to a lab, order this, and pay for it." -- the point I'm trying to make is that the system in the US is basically the same, since the ordering physician is employed by the lab testing company and you never interact with them, so it's as if they don't exist for the purposes of comparing to Greece.

Edit: I see you own a blood testing startup! Now I understand why you were surprised about the ordering physician detail. I thought you were implying that the process is difficult in some way because a doctor is involved.