The phrase "not public" implies that something is not available or accessible to the general public. There are many words that can be used as synonyms for this expression, depending on the context. Some of the common alternatives for "not public" include private, confidential, restricted, exclusive, and privileged. These words suggest that the information, location, or event is only available to a select group of people who have been granted access. Other options include hidden, obscure, undisclosed, and undisclosed, which highlight the secrecy or clandestine nature of the object in question. Ultimately, the choice of synonym depends on the tone and intent of the writer or speaker, and how they wish to convey their message to the audience.