Solved:

I used the write() method, I post a log note when the user saves their data.

def write(self, vals):
        if 'name' in vals:
            new_value = vals['name']
            old_value = self.name.id
            if new_value != old_value:
                message_body = _("%(user)s changed the Name to %(user_name)s",
                                 user=self.env.user.name,
                                 user_name=self.env['my.module'].search(domain=[('id', '=', new_value)]).name)
                self.message_post(body=message_body, message_type='notification')
        res = super().write(vals)
        return res