The term "brass hat" is a colloquial expression that generally refers to a high-ranking military officer or government official. There are several synonyms for this term depending on the context, including "bigwig," "chief," "boss," "head honcho," and "top brass." These terms are often used to describe individuals with significant authority or power within an organization or institution. Additionally, some synonyms may have geographic or cultural variations, such as "big cheese" in the United States or "top banana" in the United Kingdom. Whatever the term used, it typically conveys the same level of importance and influence associated with the "brass hat" label.