Terminology regarding missing symptom awareness depends on what is thought to be the cause. Anosognosia and other agnosias would be used for neurological disorders where self-monitoring is specifically impaired while denial, delusions and hallucinations would be used for psychiatric disorders. Denial could also be a psychiatric symptom concerning a somatic disorder. I'm not sure if other somatic fields than neurology have special terminology.

If a patient suffers from something that is not recognised as medical problem we call it hypochondria.

Not really. For example grief is not recognized as a medical problem, people suffer from it and we don't call it hypochondria.

Hypochondria is excessive worry about having a serious illness.

ETA: I think that whatever we choose to call a medical problem largely depends on our values and mere diversion from the biological norm does not a medical problem make. So the hypothetical patient could also simply disagree with others about what constitutes a medical problem.