"Finishing up" is a commonly used phrase that indicates the end of a task or project. However, there are several synonyms that can be used instead of this phrase. Some of these synonyms include wrapping up, completing, closing out, concluding, finalizing, and ending. These words can also convey a sense of accomplishment or bring a sense of closure to a project. Additionally, using these synonyms in place of "finishing up" can add variety and interest to your language and communication. So, choose the synonym that best fits your context and use it to convey your intended meaning.