Synonyms for the phrase "what day" are plentiful and can vary depending on the context. When seeking to inquire about a specific date, alternative expressions include "which day", "on what date", or simply asking "when". To determine the name of a particular day in the week, daytime, or month, one can resort to phrases like "which weekday", "what time" or "which month". However, if the intention is to know the name of a celebrated event or historical moment, alternatives may include "what occasion" or "which commemoration". Remember to adapt your wording based on the desired information you are seeking to convey.