Now, be careful the example find duplicate file names (with equal size). Not duplicate files ! Those would require check of the contents of the file.
Also there are tools like fdupe, same problem regarding remote hosts though. Some tools use xattr to store hashes. Some might use DB's. (With xattr tools, you just run the tool on the remote host first, then on the local host, if you need to save bandwith.)
I however don't have the perfect answer.
We can scan mounted drives, and Crab has a command line switch to treat names as case sensitive or not. SHA-1 calls are probably not practical across a network to compare file contents, even scans can be a bit slow, but you might do something by comparing file sizes.