You must be the Primary Contact of your organization or have officer rights to make changes to your organization. If you have these rights here are the steps to change your organization picture:
1.) Go to your organization page
2.) Click on the "About" tab on the bar underneath your organization's name.
3.) Click the blue "EDIT" button on the right side of the page.
4.) On the right of this page you will see a "Choose File" button under the words "Profile Picture" where you can upload an organization picture for your organization.