//RichTextBox rtbx = new RichTextBox();
//List<string> lstOfNames = new List<string>();

System.Windows.Documents.TextRange textRnge = new  System.Windows.Documents.TextRange(rtbx.Document.ContentStart, rtbx.Document.ContentEnd);

foreach(string name in lstOfNames)
{
    if(textRnge.Text.Contains(name))
    {
        //do your processing
    }
}