A directory that is visited by a Dired buffer in another window is by default included in the "future history" of the minibuffer that is used for file name completion; when prompted for the destination of the rename operation, use
M-p) to move through the minibuffer history until you reach the item corresponding to the directory in the other open Dired buffer.
In your case, with only one other Dired buffer open and assuming no other customizations, typing
M-n once should yield the desired destination.
It is pointed out by another answer and in Minibuffer History (GNU Emacs Manual) that:
You can customize
dired-dwim-target to prefer either the next window with a Dired buffer, or the most recently used window with a Dired buffer, or to use any other function.
That is, however, not necessary for getting quick access to the desired directory, thanks to the "future history" of the minibuffer as we saw above. Still, it may be useful should you find yourself having to type
M-n more often than not in that situation.