I don't have a problem with it. The Bond Phenomenon works based on the trust between the Pokemon and its Trainer, and Y and Croaky clearly trust each other.
As for the design, we only see the Hero Greninja that transformed from behind, and it was in a mostly-gray painting. So while it did look like Ash-Greninja, it's pretty much impossible to tell whether or not they shared the same exact appearance.
So it's technically not impossible for Croaky to turn into a different version of Ash-Greninja. Whether or not it'll happen and if it does, it'll be called Y-Greninja, is yet to be seen.
I dont understand why you of all people would suddenly fuel more of this nonsensical expectation.
The manga has been trying extremely hard at following the game's mechanics, so much as to explain Deoxys' regional forme differences and a lot more "game-y" mechanics like this to the world. The only times they betray this are when they goof up with moves (like the recent Normalize Skitty) or during the super early era of RBGY with a lot of original creations like fusion bird and super moves because there were just not enough materials.
They went out of their way to include a Battle Bond Greninja here
because there is an Ash-Greninja to showcase. It 100% won't look like Y-Greninja just because it makes more sense. If they had to screw with the rules and create their own thing, there is no reason not to simply create a Battle Bond Chesnaught too or something. Why, you mean X didn't bond enough with Chesnaught? Heck, the whole "bond with Pokemon to mega evolve them" was so badly done by all the franchise across all the media that I don't think even Kusaka has done it justice. X also hardly bonded with his mons before gauntlet showcasing their Mega Formes only during the chapters they were each caught and then the final battle.
Also the ability is literally a shoehorned thing to pander to the anime fans. Nobody besides Ash has to actually bond with their Greninja to be able to have it. It's an ability built into the Greninja. The game itself tries very hard to get around this fact by literally making BB Gren its own entity (unbreedable, un-unlockable etc). He's literally a Greninja whose ability Ash had unlocked and then given to the player "through event". The players themselves cant unlock this new ability for their own Greninjas no matter how hard they bond with them. My point is, this makes Y's Greninja having a random BB feels extremely stupid. It was as if of all the starters Sycamore gave the Kalos kid literally only that Froakie was a special snowflake because the game, which was forced by the anime, forced the mangaka to do so.
Tl;dr There won't be a Y-Greninja, it won't be called as such, and yes this is an awful way to adapt it into this manga.