General:
* Alliance: A union formed for a common purpose.
* Coalition: A temporary alliance of different groups or individuals.
* Federation: A group of states, organizations, or individuals that are united under a central authority.
* Association: A group of people united for a common purpose.
* League: A group of people or organizations that are united for a common purpose.
* Combination: A union of two or more things.
* Amalgamation: A process of merging or combining things.
Specific to labor unions:
* Labor organization: A group of workers who have joined together to improve their working conditions and wages.
* Trade union: An organization of workers who have joined together to improve their working conditions and wages.
* Guild: A medieval organization of workers who have joined together to improve their working conditions and wages.
In mathematics:
* Set: A collection of distinct objects.
In other contexts:
* Conjunction: The act of joining or uniting.
* Fusion: The act of merging or combining.
* Synthesis: The act of combining separate elements into a whole.
The best synonym for "union" will depend on the specific context in which you are using the word.