Assuming you have the original document:
var doc = XDocument.Load(...);
then create a new element (not a document)
var newElement = new XElement("books",
new XElement("Signature_Key", Signature),
new XElement("License_Key", Licencekey),
new XElement("Company_Name", ComapnyNam),
new XElement("Machine_Name", Machine_Name);
new XElement("Date_And_Time", DateAndTime.Now);
And then insert it:
doc.Element("stock").Add(newElement);
doc.Save(....);