overwrite the Name field

When registering, the user entered the first and last name Joanna Smith. This is reflected in the lastname and firstname lines. Accordingly, in the user panel, her Name is listed as Smith Joanna .

Then she changes her last name to Johnson. I made a separate field cb_change_lastname and autoactions with overwriting the lastname field. The value in the lastname field became Johnson, but the Name field remained the same as Smith.

How can I overwrite the Name field ?

Why are you copying the name to another field? Sorry, don't understand what you're trying to do.

When registering , the user fills in the fields lastname (Smith), firstname (Joanna). On the site, the Name field consists of these two fields (Smith Joanna) . After a while, she changes her last name to Johnson and asks to change it.

A new last name is inserted in the last name field, but the Name field does not change the last name and the user is listed as Smith Joanna, not Johnson Joanna.

How do I solve the problem of changing the Name field?

That should never be an issue. The Name field is always populated when first, middle, or last name fields are changed unless something is interrupting that process. I was not able to confirm any issue with this behavior. How are your users editing themselves? They should be exclusively using CBs profile edit.

The replacement is auto actions. Fill in the field with the new last name, upload a document confirming the change of the last name and overwrite it

So you're adding the new last name to a custom text field? If that's the case that explains your issue since it's a custom field it's not considered for name construction. You don't need a separate name field for this. You can use CB Conditional to show your document file field (make it required) if the lastname fields value changes. This is done using the below condition on your file field.

Display: Field conditional show
Field: Last Name (lastname)
Operator: Not Equal To
Value: [lastname]
Locations
Registration: No
Profile Edit: Yes
Profile View: No
Userlists Search: No
Userlists View: No

Now if they try to change lastname the file field should show up and since it's required they'll have to provide the documentation to change the lastname. This will keep all name fields properly in sync and won't require another text field.