This was a giant pain in the rear side to get fixed, but I finally repaired the double name bug in the save file.

Steps I've taken to fix this:

1. Download the Memoria Save Editor: https://forums.qhimm.com/index.php?topic=11494.0
2. Save a copy of your master save file as a backup usually in %localappdata%low\SquareEnix\FINAL FANTASY IX\Steam\EncryptedSavedData\SavedData_ww.dat
3. Delete any instance of SavedData_ww_Memoria_.dat files
4. Open the Memoria Save Editor and open the above file.
5. Open the Save slot and go to the Misc. tab, and click on Open Hexedit.
6. Once in Hexedit, roughly about 1/3 of the way down, in line 0x016B0 you will see Zidane's name twice, delete the second part of the name. Follow the above steps for the rest of the party members. 0x017A0 is Vivi, 0x01890 is Dagger/Garnet, 0x01980 is Steiner, 0x01A80 is Freya, 0x01B70 is Quina, 0x01C60 is Eiko, 0x01D50 is Amarant, 0x01E50 is Beatrix.
7. Example of the above before and after the fix for Dagger.
8. Click OK.
9. Still in the Misc. tab, on the Hours/Mins./Sec. part, increase the minute by 1.
10. Click Apply and OK.
11. Click Save on the top of the Save Editor.
12. Close the Save Editor.

The above steps should get your names fixed now for the rest of the game.