X:
While it's true that Final Fantasy Adventure is the first of the Seiken Densetsu games, it IS also a Final Fantasy game. The full Japanese name of the title is Seiken Densetsu: Final Fantasy Gaiden, not just Seiken Densetsu, so, no, it's not true that the name Final Fantasy was just added for name recognition, it was already there as the subtitle in the original Japanese release. The game has numerous Final Fantasy elements: chocobos, moogles, red mages, white mages, dwarves, etc.--it's very clearly a Final Fantasy inspired work. Those elements were, of course, downplayed in the sequels. Bear in mind that Squaresoft had no way of knowing whether this more Zelda-esque title would even be a hit when they made it, and thus, wouldn't have had any immediate plans for sequels at the time of its development.
Gameboy Final Fantasy Legend 1-3, on the other hand, (Makaitoushi SaGa, SaGa II: Hihou Densetsu, and SaGa III: Jikku no Hasha, respectively, in Japan) have nothing to do with Final Fantasy and did just have the more popular Final Fantasy moniker pasted on them for the North American (and presumably European) audiences.