“Sith Eternal” is a name I can live with. It explicitly states the Sith nature of the faction, bringing the story of the saga full circle (back to the essential Jedi-Sith conflict) and it doesn’t recycle either Empire or Order. But I think maybe some dialogue tweaking could serve to further establish that the First Order is either subservient to, or merged with, the Sith Eternal/Final Order. The distinction between the two organisations is not very clear when taking only the film as reference.
The only thing I’ll defend about the name “Final Order” is it helps establish the painstakingly dumb name of the First Order. These were phases for his return. It would be great if there was a way to adjust the line to be the “Final Order of the Sith Eternal” or something similar.