Batch renaming is done the same way renaming individual files is done: One MoveFile call per file, with the old and new names passed to it. The NAS should not see a difference, other than in how fast the renames are happening.
A quick test against a network drive here works fine as well.
Could you post a screenshot showing how you have the Rename dialog set up, ensuring we can see the preview of what will happen at the bottom of the dialog?
A Process Monitor log of what happens when the batch rename is applied may also reveal what's going on.
Have you tried refreshing the folder (usually F5) after renaming the files to see if they're being renamed but the change notifications are not reaching Opus?