Instead of message box after rename completion, check for matching name before opening initial type rename dialog and add checkbox to it, which specify if file should be renamed to match type name. If type name matches file name before rename, checkbox should be checked initially, otherwise unchecked.
This way, user does less one hit during rename of already synchronized file, can skip synchronization or force synchronization, even if file and type initially has different names (not currently doable by Resharper).