Background/Objectives: The Omicron variant of SARS-CoV-2 is undergoing constant mutation. New strains vary in neuropathogenicity and the neurological spectrum of disease. The aim of this study was to assess the frequency and clinical characteristics of neurological manifestations during the Omicron dominance among hospitalized patients, including the differences between three subsequent periods. Methods: This retrospective single-center study included 426 hospitalized adults with confirmed COVID-19 divided into three periods (O1, O2, and O3) dependent on the dominance of Omicron subvariants in Poland. Demographic and clinical data, in particular neurological manifestations, were collected and compared. Results: The median age of the group was 74, older in subsequent (later) periods. The number of patients with a history of previous SARS-CoV-2 infection or vaccination increased with the duration of the pandemic. The severity of COVID-19 became lower in successive periods. Neurological manifestations were observed in 55.4% of patients, and the most frequent were delirium, headache, myalgia, dizziness, cerebrovascular diseases, and encephalopathy. In subsequent periods of Omicron dominance, a higher frequency of neurological manifestations such as delirium, transient ischemic attack (TIA), and encephalopathy was observed. Headache or myalgia was related to a shorter hospitalization while delirium, cerebrovascular diseases, and ischemic stroke were linked with an increased risk of death. Conclusions: The Omicron variant of SARS-CoV-2 presents a wide spectrum of neurological manifestations. Although there is an improvement in the survival rate of patients with COVID-19, the frequency of neurological manifestations increases. The occurrence of delirium, cerebrovascular diseases, and ischemic stroke results in higher mortality.