You’re close, but you want name to be an XAttribute
rather than XElement
:
XDocument doc = XDocument.Load(spath);
XElement root = new XElement("Snippet");
root.Add(new XAttribute("name", "name goes here"));
root.Add(new XElement("SnippetCode", "SnippetCode"));
doc.Element("Snippets").Add(root);
doc.Save(spath);