Spanish translation: Enfermedad de Addison o Hipoadrenocorticismo
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Explanation: It's the disease that results from lack of enough cortisol and related hormones.
As far as I know, "insuficiencia suprarrenal" remains the same for Veterinary Medicine. As for "Addison's", I'd reserve it for the human form. The name comes from Mr. Addison, who describe the skin changes in humans with IS.