Word for the opposite of "hypochondriasis"

I think egosyntonic comes reasonably close:

Egosyntonic is a psychological term referring to behaviors, values, feelings that are in harmony with or acceptable to the needs and goals of the ego, or consistent with one's ideal self-image.

Many personality disorders are considered to be egosyntonic and are, therefore, difficult to treat. Anorexia nervosa, a difficult-to-treat Axis I disorder, is also considered egosyntonic because many of its sufferers deny that they have a problem.

Its counterpart is egodystonic.

A widely used antonym for hypochondriac is "stoic." Spelt without a leading capital, it doesn't refer to the Stoic school of philosophy but to the general idea of ignoring or minimizing setbacks and unfavorable information.

la belle indifférence

A naive, inappropriate calmness or lack of concern in the face of perceptions by others of one's disability, often seen in those with conversion disorder but no longer considered pathognomonic for conversion disorder.

This is obviously a French term, but it’s widely used in the English-speaking medical community. As alluded to in that definition, it was originally applied to a specific group of psychiatric patients, but it is now known that it is not specific to conversion disorder. The term is frequently applied to describe the inappropriate neglect of physical symptoms of any cause.

(Of note, egosyntonic, proposed in another answer, is, as far as I know, used exclusively in reference to psychiatric pathology.)