Based on a quick glance of the API documentation it looks like TMDM/OMDB doesn’t receive your filenames, they use unique IDs assigned to their shows and potentially searches based on titles/episode numbers that Jellyfin is already aware of.
Even if Jellyfin used the filename to search OMDB/TMDB, the headers, body, and the path of the URL (api.themoviedb.org/<path>) are all encrypted by the TLS connection so would not be visible to your ISP.
If you’re open to things similar to Plex, I’d recommend Jellyfin! Plex has been making some decisions lately that aren’t necessarily selfhoster friendly. A selfhosted instance of Plex still authenticates using Plex’s central servers (if you’re internet is out or Plex is down and you want to stream your own movies or shows, that won’t work due to failed authentication). That’s compared to your Jellyfin instance handling authentication locally. If you can contact your server, you can watch your media. Plex has also announced a credit skipping feature, uploading credit timing to their central servers that can be restored on complete rebuild. While they say it’s anonymous, they need some way to associate you and the proper credit timings, to send that back to you.
Jellyfin is earlier days in development, and you should check to see what clients are available to see if that would work with your hardware. But Jellyfin is definitely catching up, I’ve been very happy with their server and applications.
It’s all about what you value, and supporting the things you love (or rely on, in a more utility sense). I’d value the speed, the lack of data collection that may be used against a user, the speed, the location options, and that same provider being in business for time to come. When I’d need a good VPN, nothing else will do. That seems worth the couple of USD per month to me, whether that VPN is for obscuring traffic I don’t want others to know about (whether it’d be because of those facilitating the connection or the other end of the connection).