TransferSpreadsheet is indeed the way to go, but naming the sheets in
the workbook in advance will not do the job! "Next available" is
probably misleading; any existing sheet, whether having any data in it
or completely blank, is not considered available as per the quote from
help above. At the first export Access will create a new sheet and name
it after the exported table or query, then from the second export on it
will overwrite that same sheet.

The trick here is to use the "Range" argument, in spite of help saying
it is not used in export; the argument passed will be the name of hte
sheet created (if none exists by that name) or overwritten (if the name
already exists).

Also note that there is no need to create the workbook manually up
front, if it does not exist Access VBA will create it for you.

By the way, if territory is always going to be 1 trough 10, there is no
point in changing the territory parameter and exporting manually. Use
some simple VBA code to do it all for you! Sample:

Function export_territory_data()
Dim sQuery As String, sFile As String
sQuery = "MyQuery" 'Name Of Query To Export
sFile = "C:\SomeFolder\SomeFile.xls"  'Target path and file name
For i = 1 To 10
    Forms![FormName]![ControlName] = i 'put actual names here
    DoCmd.TransferSpreadsheet acExport, acSpreadsheetTypeExcel9, _
        sQuery, sFile, True, "Territory " & i
Next
End Function

As long as you have the form open when you execute the code, it will do
the rest. You could add a command button on the form to trigger the
code; in that case, paste the code directly in the button's Click event
(skipping the first and last line).

HTH,
Nikos