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Loop through xml resetting var on each loop
XmlNodeList nodes = reports.SelectNodes("Reports/namespace");
        foreach (XmlNode NSpace in nodes)
        {
            List<string> newlist = new List<string>();

            //loop through checks one by one.
            foreach (XmlElement element in reports.GetElementsByTagName("report"))
            {
                doStuff
            }
         }

foreach (XmlElement element in reports.GetElementsByTagName("report"))

<Reports>
    <namespace Type="first">
    <report>
    <name>first_1</name>
    </report>
    <report>
    <name>first_2</name>
    </report>
    <report>
    <name>first_3</name>
    </report>
    </namespace>
    <namespace Type="Second">
    <report>
    <name>Second_1</name>
    </report>
    </namespace>
    <namespace Type="Third">
    <report>
    <name>Third_1</name>
    </report>
    </namespace>
    <namespace Type="Fourth">
    <report>
    <name>Fourth_1</name>
    </report>
    </namespace>
    </Reports>

XmlElement namespaceElement = (XmlElement) NSpace;
foreach (XmlElement element in namespaceElement.GetElementsByTagName("report"))
{
    // doStuff
}

foreach (XmlElement NSpace in nodes)
{
    List<string> newlist = new List<string>();

    foreach (XmlElement element in NSpace.GetElementsByTagName("report"))
    {
        // ...
    }
}