Background: Human Immunodeficiency Virus (HIV) infection represents a significant public health concern and, consequently, the incidence of HIV-Associated Neurocognitive Disorder (HAND) has grown over the years. The present study aims to assess HAND with the Montreal Cognitive Assessment (MoCA) in People Living With HIV/AIDS (PLWHA) to find significant associations with cognitive impairment. Methods: The study included 210 PLWHA, aged from 30 to 81 years, of whom, 137 (65.2%) were males. They were assessed at the Immunology Service of the University Hospital of Monserrato, Cagliari, Italy, between November 2022 and April 2023. Results: The sample showed an overall optimal response to antiretroviral therapy, as shown by the excellent levels of CD4+ lymphocytes and HIV RNA copies. A sum of 115 subjects (54.8%) were considered cognitively impaired and the multivariate analysis demonstrated that it was independently associated with duration of infection (OR: 0.96), age (OR: 1.12), alanine aminotransferase (ALT) (OR: 1.02), and depression (OR: 1.33). By dichotomizing the variables, the significance of the association was confirmed for age (65-year threshold) (χ²: 5.142, p = 0.0233) and depression (χ²: 7.834, p = 0.0051). Conclusions: Our study demonstrates that it is hard to find both statistically and clinically significantly associated variables with cognitive impairment in PLWHA, and that the strongest independent association is with depressed mood.