I renamed about 80 Home Videos files in Finder (Movies/TV/Media.localized/Home Videos). The TV app on my Mac, and my Apple TV reading the same library through Home Sharing, kept showing the old titles. Restarting the Apple TV did not help.
Fix that worked for me, without removing and re-importing anything:
Step 1: In the TV app on the Mac, open Library > Home Videos.
Step 2: Press Command-A to select all the videos.
Step 3: Right-click > Get Info, and confirm the prompt about opening many items.
Step 4: Change nothing, just click OK.
All titles refreshed to match the new file names. The TV app seems to keep its own library database and only re-reads a file's information when the item is touched (Get Info or playing it), so renames made in Finder are not picked up automatically. Posting this in case it helps someone else.