If you are the Alliance Leader, you are able to change the alliance emblem by following these steps:

1. Go to the home screen of the game.
2. Find and tap ALLIANCE.
3. Tap the Alliance Members button.
4. Tap the "Edit" button.
5. Tap the icon under Emblem to bring up a list of other icons. Select the new icon
6. Tap the "Select" button.
7. Tap the "Confirm" button.

You should see the changes immediately.