The frame indicates which item has keyboard focus, which is not always the same as selection.
F2 in Opus does a single-file rename of the item with keyboard focus. (It can also rename multiple files at once, similar to Explorer, but that's really just for compatibility with Explorer and a very simple multi-file rename like Explorer's, because people asked for it.)
If you select multiple files and click the Rename button (or Ctrl+3 hotkey by default), that will open the Rename dialog for renaming multiple files at once in a much more powerful way. The files in that will be the selected files, not the one with keyboard focus (unless it's also selected, of course).
I performed a few other tests and I'd like to apologize and rectify something (I should have triple-checked before posting ):
The behavior merely seems to happen if doing a marquee selection on only one file that doesn't have the keyboard focus:
So, on two or more files which none of them has the keyboard focus, rename (F2) will work for the highlighted files despite the fact that, as seen on the images below, it's the one that has the focus on which looks like to be renamed (but won't be in the end):
In the end, I could simply select one file/folder by clicking on it instead of performing a marquee selection (I understand that a marquee selection for only one file might seem odd, but it's just a very old habit I have in a certain situation).
Or, as suggested by Leo, to use the DOpus Rename function instead (I usually whether use the F2 or the Ctrl+3 rename functions depending on the situation).
P.S. By the way, what an outstanding community there is on this forum. Thanks a lot for your fast replies!