/*

    
        John
        Smith
    
    
        James
        White
    

*/

XmlDocument xml = new XmlDocument();
xml.LoadXml(myXmlString); // suppose that myXmlString contains "..."

XmlNodeList xnList = xml.SelectNodes("/Names/Name");
foreach (XmlNode xn in xnList)
{
  string firstName = xn["FirstName"].InnerText;
  string lastName = xn["LastName"].InnerText;
  Console.WriteLine("Name: {0} {1}", firstName, lastName);
}