I recall an interview, though I can't recall if it was a general event or a PLL, where they discussed the naming conventions and how they considered the traditional suffix-based naming but ultimately chose to use numbers instead, so as to make the game more accessible to non-FF lifers. You and I know Fire<Fira<Firaga<Firaja, but someone who's only ever played WoW or TOR would take a minute to figure that out. But for the Japanese, they got Cure, Cura, Curaga.
Interestingly enough, the HW WHM abilities are actually named the same in JP and EN. Asylum, Assize, and Tetragrammatron aren't just NA/EU localizations of traditionally-named abilities.
(You can look up Job Quests > White Mage on the Lodestone and then change the subdomain of the URL from na.finalfantasyxiv to jp.finalfantasyxiv to compare, if you feel so inclined and can read kana).

Originally Posted by
Eloah
The main thing that got me thinking this was my run of Lost City HM today, It finally clicked that the final boss casts Cure 4, so why not us?
One of the things about Lost City is that it demonstrates what was discussed earlier in
the WHM questline, where the padjal doesn't want to accept you as a WHM because he thinks you'll just abuse White Magic. I don't recall off the top of my head how long it's been, but the abuse of White Magic that lead to the fall of Amdapor was at least long enough ago that your typical CNJ doesn't recognize the existence of anything after Cura/Cure2, and certainly you can see how even spells that we as modern WHMs are familiar with have changed since then. The Amdapori Regen, for example, looks nothing like what we would call Regen. While I can't speak for the lore team or anyone who actually worked on the game, it makes sense that the de-/re- evolution of White Magic over the years could easily explain changes in names and such. A WHM of our day, not necessarily privy to the attack names we players see in combat, might go into Kuribu's chamber and call what he sees "Asylum" instead of "Regen". Unless he was some sort of Historical Magickalist or some academic profession that came with an understanding of how time affects magical theories and repertoires.