Yes you can do it with the data from two fields.where firstname and lastname
are the names of the associated form fields.

Sub SaveForm()
Dim fName As String
With Active Document
   fName = .FormFields("LastName").Result
   fName = fName & .FormFields("FirstName").Result & ".doc"
   .SaveAs fName
End With
End Sub

Run on exit from whichever field is completed second of the two fields (or
from a later field)

Double click the field with the form unlocked and assign it to the Run Macro
on Exit property.

The macro works with Word 2007, assuming of course that there is content in
the UserID (legacy field) text field. The following will error trap no
content:

Sub SaveForm()
Dim fName As String
On Error GoTo Noname
With ActiveDocument
   fName = .FormFields("UserID").Result & ".docx"
   .SaveAs fName, FileFormat:=wdFormatDocumentDefault
End With
Exit Sub
Noname:
MsgBox "UserID field is empty"
End Sub

If you want to use the content of a bookmark then

Sub SaveForm()
Dim fName As String
On Error GoTo Noname
With ActiveDocument
   fName = .Bookmarks("UserID").Range.Text & ".docx"
   .SaveAs fName, FileFormat:=wdFormatDocumentDefault
End With
Exit Sub
Noname:
MsgBox "UserID bookmark is empty"
End Sub

or you could use the built-in document properties

Sub SaveForm()
Dim fName As String
On Error GoTo Noname
With ActiveDocument
   fName = ActiveDocument.BuiltInDocumentProperties("Author") & ".docx"
   .SaveAs fName, FileFormat:=wdFormatDocumentDefault
End With
Exit Sub
Noname:
MsgBox "Author field is empty"
End Sub