How to create a top level xelement with multiple xelement nodes in a foreach loop

I am looking to create a top level XElement with multiple XElement child nodes as below.

<Names>
    <Name>
        <firstname>Mike</firstname>
        <lastname>Smith</lastname>
    </Name>
    <Name>
        <firstname>Sam</firstname>
        <lastname>Smith</lastname>
    </Name>
    <Name>
        <firstname>Michelle</firstname>
        <lastname>Smith</lastname>
    </Name>
</Names>

If I go with something similar to below, how can I append the child elements ( elements) to a top level element ? Thanks for any suggestions.

for (int i = 0; i < 10; i++)
{
    var str = Getelement(i);
    //str is a string that contains xml
    XDocument doc = XDocument.Parse(str);
    XElement root = doc.Root;
    //root will contain <Name>
}