If I've understood, in your code, just before you create the name element you need to check whether or not the "txtName" has any content, if not do nothing with name element otherwise do as now.
The steps are:
1) Load doc
2) If successful go to step 4
3) Create doc with just <root/>
4) Select name node
5) If txtName has content replace content otherwise ignore
6) Add phone numbers
Steps 4 and 5 are done like this after loading doc into objDom
Code:
sName = Request("txtName")
Set oNameNode = objDom.selectSingleNode("/root/Name")
If Len(sName) > 0 Then
oNameNode.text = sName
End If
Joe (MVP - xml)