There is no way to absolutely prevent people from using your organizational names, logos, branding, identity, and other copyrighted materials on social network sites (besides creating groups on every social network under every conceivable organization name, which is impractical).

The best way to combat infringements is to:

  1. First, kindly ask the person who made the group to take it down.
  2. Second, ask the social network (most of the big ones have this) to take down the group/account, or at least restrict access, by filing a copyright/infringement claim.
    Facebook: Copyright Infringement Policies
    Twitter: File a copyright or DMCA take-down notice
  3. (If it comes to this) File a lawsuit against the social media site, or the individual who created the group/account. This is obviously expensive, and unless you've gone through the DMCA claim as stated above, don't expect to get far with this method.

It's a pain, but it's something we will all need to deal with more often these days...