Mike was telling us:
Mike nous racontait que :

Instead of renaming the formfields already in place, you should rename the
one you just inserted in the document before you fill them out with text.
The reason being that if you insert formfields that have the same name as
exiting formfields, Word will internally choke and if you try to run simple
code like:

    myFormField.Name = "Test" & i

Word will return an error on those fields that had conflicting names.

There is a workaround (my code below) but that removes the formfield content
and resets it to its default value. This is fine with fresh formfields that
do not have content yet, but not with existing ones.

'_______________________________________
Sub RenameFormfields()

Dim lngSecNumber As Long

If Selection.Sections.Item(1).Index = 1 Then
   MsgBox "You cannot use this procedure from the first section in the
document."
   Exit Sub
End If

lngSecNumber = Selection.Sections.Item(1).Index

With ActiveDocument.Sections(lngSecNumber).Range
   .FormFields(1).Select
   With Dialogs(wdDialogFormFieldOptions)
   .Name = "Name" & lngSecNumber
       .Execute
   End With
   .FormFields(2).Select
   With Dialogs(wdDialogFormFieldOptions)
   .Name = "Place" & lngSecNumber
       .Execute
   End With
End With
'_______________________________________

But, if you use a "clean" system, you can use something like:

   myFormField.Name = "Test" & i

For that to Work, create an Autotext with the formfields, the text and the
section break and name those formfields "Name" and "Place".

Insert them in the first section and run code like:

'_______________________________________
Dim lngSecNumber As Long

lngSecNumber = Selection.Sections.Item(1).Index

With ActiveDocument.Sections(lngSecNumber).Range
   .FormFields(1).Name = "Name" & lngSecNumber
   .FormFields(2).Name = "Place" & lngSecNumber
End With
'_______________________________________

Every time you insert a new section, run the code to rename the formfields.
This way you will never have conflicting names.