Oh! So you only want a copy of the latest file in each directory to be backed up. In that case, rsync probably isn't what you want. It'll be a little more complicated than that.
If the files are named with that date format, you'll have trouble sorting them properly based on that, so you'll probably want to use the file creation time instead. You can use 'ls -t' to sort the directory listing and grab the most recent one. I'd recommend trying it a few times to make sure it gives you the result you're looking for.
Then there's what to do on the remote system... Do you want to simply delete what's there first, and then replace it with the most recent file, or do you want to transfer the new files first, and then determine what needs deleted?
For the transfer, you'll probably want to use something like rsync or 'scp', but ftp could work as well. I tend to use scp with key-based authentication so that it can be automated without requiring you to enter a password every time.
You could also mount the remote filesystem with NFS or sshfs so that it can be treated like a local filesystem. That might be easier in this case, since you may have to script the removal of the OLD backup files.