I'd recommend you look into hardlinking or possibly symlinking. This is what Radarr and Sonarr do.
Radarr and Sonarr (along with other "arr's" such as Prowlarr - for tracker management - and Lidarr/Readarr) are all management and automation tools.
I suggest you look into the applications and
https://trash-guides.info - I contribute to the guides and we have loads of tutorials on all of the basics you'd need.
Renaming the torrents in the client, in my opinion, should be a last resort. You can setup jellyfin, plex, emby, etc to hardlink (which makes a reference "file" identical to the original on the disk without consuming any extra space. Symlinks do similar, but are merely a "shortcut" to the file which something can reference - however with hardlinks until all references to the file are gone, the file will remain on disk and consume one file's worth of space. Symlinks rely on the original file being there - think of it like pointing a shortcut on your desktop to a exe that no longer exists.
The idea would essentially be, if you don't want to use an automation tool, use something like filebot and just have it sort and organize your media anyway you like and tell it to hardlink or symlink this data depending on your desire for continuing to seed or deleting seeds, and point your media server at the organized folder.
You can customize something like filebot or "arr" to name it however you like.
If this works for you, by all means do you, it's your setup not mine. I just thought that given the problem you are trying to solve a easier and more streamlined approach might be worth mentioning.
I'd recommend you check out trash's guides - which I contributed the deluge guide and any deluge-related guides - as well as other things, and check out Radarr, Sonarr, and Prowlarr.
We have a discord for the guides and set up if you have questions or need help, if you want to go down the automation route.