We had a similar situation. Even though HIPAA doesn’t apply when a visitor posts on your Facebook page, we still don’t what that type of content on our page so we approve all tagged posts before they can be shown on our page. You can do this under Settings –> Visitor Posts –> check the box for “Review posts by other people before they are published to the page”
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I have the same branding problem at my company. Here is an example of how I took two logos and saved it as one image to upload on their website where our facility was being supported by a foundation. I added a blank strip in the middle so people could see they were two seperate logos. You might be able to see it better on their website http://www.LakeSideOasis.org in the top left corner.