How to add namespace to xml using linq xml

When you write

XNamespace ns = "xsi";

That's creating an XNamespace with a URI of just "xsi". That's not what you want. You want a namespace alias of xsi... with the appropriate URI via an xmlns attribute. So you want:

XDocument doc = XDocument.Parse(framedoc.ToString());
foreach (var node in doc.Descendants("document").ToList())
{
    XNamespace ns = "http://www.w3.org/2001/XMLSchema-instance";
    node.SetAttributeValue(XNamespace.Xmnls + "xsi", ns.NamespaceName);
    node.SetAttributeValue(ns + "schema", "");
    node.Name = "alto";
}

Or better, just set the alias at the root element:

XDocument doc = XDocument.Parse(framedoc.ToString());
XNamespace ns = "http://www.w3.org/2001/XMLSchema-instance";
doc.Root.SetAttributeValue(XNamespace.Xmlns + "xsi", ns.NamespaceName);
foreach (var node in doc.Descendants("document").ToList())
{
    node.SetAttributeValue(ns + "schema", "");
    node.Name = "alto";
}

Sample creating a document:

using System;
using System.Xml.Linq;

public class Test
{
    static void Main()
    {
        XNamespace ns = "http://www.w3.org/2001/XMLSchema-instance";
        XDocument doc = new XDocument(
            new XElement("root",
                new XAttribute(XNamespace.Xmlns + "xsi", ns.NamespaceName),
                new XElement("element1", new XAttribute(ns + "schema", "s1")),
                new XElement("element2", new XAttribute(ns + "schema", "s2"))
            )                         
        );
        Console.WriteLine(doc);
    }
}

Output:

<root xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
  <element1 xsi:schema="s1" />
  <element2 xsi:schema="s2" />
</root>