Tell me, please, what is the name of the disease when, under stress, a person begins to limp (in a normal state, a person has a stable gait)?

Depends on what you mean by "stress". As answered above, then perhaps this is a manifestation of psychosomatics. But I have variations on the theme that states of unstable gait, lameness, astasia - abasia are often found in conversion disorders (hysteria). To say exactly what causes such symptoms and whether it is precisely related to stress (because after that does not mean in consequence), a more complete clinical picture and examination of the patient are needed. And, of course, neurological diseases should be ruled out.

In short,

Psychosomatic diseases (from ancient Greek ψυχή - soul and σῶμα - body) are a group of painful conditions that appear as a result of the interaction of mental and physiological factors. These are mental disorders manifested at the physiological level, physiological disorders manifested at the mental level, or physiological pathologies that develop under the influence of psychogenic factors.