There are several synonyms that can be used for the phrase "just finished." Some of the common ones include completed, concluded, ended, finalized, wrapped up, terminated, finished off, and brought to a close. Each of these phrases carries a slightly different connotation and can be used in different contexts. For instance, "completed" is often used to describe a task or project that has been successfully accomplished, whereas "ended" and "brought to a close" might be more appropriate for describing a final chapter or the closing of a door on a chapter of one's life. Nonetheless, all of these synonyms can be used interchangeably to convey that something has come to an end.