I’m looking at using my RPI to sync some folders across two NAS devices I have and I was wondering if this would be the way to go.

Basically, I want to know how it handles the syncing… If I modify a file name will it just rename the file on the target drive or will it just create a new file and remove the old one?

If it doesn’t do this how would I easily go about syncing using my RPI? (For reference I used to use Sync Toy for windows but would like to eliminate this)

Have a look at Syncthing.

DietPi-Sync uses Rsync.
Rsync is very efficient as it only modifies “chunks” of the files that needs to be updated, rather than replacing the whole file each time.

DietPi-Sync is great for syncing 1 source and target location. If your planning on syncing multiple sources and targets, John’s suggestion is good advice: