The X-ray people make sure that you are identified properly. The date on which the X-ray was taken is printed in the corner of the X-ray film, along with your name and date of birth.
So it's unlikely that there could be a mix-up. But if there was a mix-up the doctor would soon realise. If you had a broken arm and the X-ray showed a stomach then the doctor would know that it was the wrong X-ray.
If the X-ray doctor makes a mistake then the doctor who is treating you will notice. If your doctor needs help then your doctor will ask another doctor for help.
If it's still not clear what the test means then they will do it again--perhaps later, after things in your body have changed.