Hypogonadism is low production of sex hormones. In men it refers to low testosterone together with symptoms.
A key distinction: true (pathologic) hypogonadism comes from disorders of the hormonal axis and generally needs lifelong testosterone replacement, whereas the mild low testosterone common in obesity is usually reversible — driven largely by reduced SHBG and often corrected by weight loss. See the guide on HRT for men and GLP-1 medications.