You can also read deeper into it if you want. I doubt any of this is really intentional, but it's interesting to think about.

The word "final" (and various synonyms thereof) can also be used to mean "ultimate" in Japan. In fact, one of the definitions of the word "ultimate" actually IS final. Extending the metaphor further, there is an overused phrase that goes "I am the alpha AND the omega". Alpha and omega are the first and last letters of the Greek alphabet respectively. Omega in this sense means last, but it also sort of means "biggest".

In every game, something happens that threatens to bring about the end of the world. that definitely carries a sense of finality. It's almost implied that the title refers to the events of the game. As in, "these events would be the final fantasy that this world will have". I know it's kind of reaching but that's how I think about it.