When you create your own union, you automatically become its leader and can choose the name and the emblem. Also, the leader has power to accept new members or remove old ones.
It’s possible to create a union in the early stages of the game, as well as after you’ve joined another union. If you’re not in a union, and want to create one, open the chat.
Then press the Create your Union button in the lower part of the panel.
If you’re already a member of a union, open the main window by pressing on the Island on the horizon. Then open the settings menu and press the Create your Union button.
In the window that opens, write the name of your union, select the color, emblem and frame, and define the union’s type.

Note that all points you have earned while being in the union will be reset after you create your own union!