
Files are not identified by names actually, but by a unique signature. Unison has no problem renaming files and directories. This makes sense because your catalog is a SQLite database (a SQL db on disk) for performance reasons it is in the database engine's best interest not to shuffle every bits around.

Granted, bigger changes happen in your LR catalog, but never quite big enough that they require to send the whole file over. For example, if I modify the Artist name on a MP3 or add some keywords to a JPEG file, it will not send the whole song or photo over, but only a very small portion of it. It will instead transmit a smart, compressed subset (a delta) representing the difference between both files. If a large file has been updated (say, your LR catalog), it will not copy the whole file over. This later point is relevant to your problem. Transfers of small updates to large files are optimized using a compression protocol similar to rsync.

It allows two replicas of a collection of files and directories to be stored on different hosts (or different disks on the same host), modified separately, and then brought up to date by propagating the changes in each replica to the other. Unison is a file-synchronization tool for Unix and Windows. As a software engineer, this is one of the top 3 pieces of software I use daily and can't live without. Once it is up and running, it is very easy to work with and it will perform its duty quickly and effortlessly.

I'll be honest though, this is not a tool a lot of people use, it is not trivial to setup but it will solve your problem. This includes my LR catalogs and pictures since I started photography. I've been synchronizing collections spanning up to 60GB and ten thousands of small and large files for years now.
