Json.net rename properties

I have a string representing JSON and I want to rename some of the properties using JSON.NET. I need a generic function to use for any JSON. Something like:

public static void Rename(JContainer container, Dictiontionary<string, string> mapping)
{
  foreach (JToken el in container.Children())
  {
    JProperty p = el as JProperty;
    if(el != null && mapping.ContainsKey(p.Name))
    {
      // **RENAME THIS NODE!!**
    }

    // recursively rename nodes
    JContainer pcont = el as JContainer;
    if(pcont != null)
    {
      Rename(pcont, mapping);
    }
  }
}

How to do it??