Let me preface this post with this: I personally don't believe that when Luffy and co get to Laugh Tale, it's going to be one massive info dump. Rather, I think Oda is leaving breadcrumbs and puzzle pieces for the readers that will come together in our heads when they reach Laugh Tale and we'll be like "OH MY GOD! THAT'S IT!" Otherwise, the final island is just gonna be exposition for however many chapters it is.
Now with that being said, I have a feeling that one of the breadcrumbs Oda will drop before Laugh Tale will be the name of the ancient kingdom and it will happen during Wano. Why do I think that? Well, Wano is the convergence point for some of the oldest things in the world of One Piece. We have Zunesha, Toki, the Poneglyphs, the Ancient Weapons and Wano itself which has all but been stated to have been a major player during the Void Century.
Zunesha
Zunesha is the oldest living creature in the world of One Piece. We know it's sentient and therefore, it must know things, specifically, everything that has happened in the 1000 years it's been alive. In chapter 1040, we learn that Zunesha was a companion or nakama (depending on the translation?) of Joyboy's. This makes Zunesha easily the most concrete proof besides the Poneglyphs of what happened during the Void Century and since he is capable of speaking to people, the greatest source of lore I think we've gotten in the story.
If Zunesha is telling Momo that he was a companion of Joyboy and Joyboy is closely associated to the Ancient Kingdom, I don't see how Zunesha doesn't know its name. It's entirely possible then that Momo has already learned it from their conversation in 1040 or even their conversation back during the Zou Arc.
Toki
Now according to the story, Toki was born around 830 years ago (during the Void Century) and was part of the Amatsuki daimyo family of Wano BUT she had never been to her homeland. Hence, why she was curious about it when she first met Oden and why she was traveling through time to get there. So what does this mean? It means that during the Void Century, Toki was somewhere else besides Wano. Where was that somewhere else? Likely, the ancient kingdom.
830 years ago was right at the tail-end of the Void Century which means that the great war that established the World Government was either ongoing, about to begin OR finishing up right before Toki went forward in time. Now we can assume she wasn't an ally of the WG because why would she travel in time if her side won? So it's highly likely that she was an ally of the Ancient Kingdom and therefore, knows its name.
I think it's possible Toki told Oden the name of the Ancient Kingdom and it may even be in his logbook.
Poneglyphs
Wano is the homeland of the Kozuki Clan, the inventors of the Poneglyphs and we know that there are at least 3 there. The Road Poneglyph that Kaido possesses, the blue one in the Skull Dome that Law found and the blue one in Orochi's castle that Brook found. Considering Wano and the Kozuki are so closely tied with the Void Century, I figure the two blue Poneglyphs have some major lore written on them and so far, the only person capable of reading them hasn't gotten to take a look at them yet. Which leads to my next point...
Robin
This is also why I think think the capture of Robin has been played up so much during the Wano Arc. As far as we know, Robin doesn't know the Ancient Kingdom's real name but we know she was a scholar of Ohara. We also know that the WG was so scared of letting someone even speak the name that they silenced Prof Clover on the spot.
I speculate that the WG wants Robin so badly, not only because of the Ancient Weapons but because if she learns the name of the Ancient Kingdom, with her Oharan knowledge, she is going to be able to put some pieces together relatively quickly. After the raid is said and done, Robin will get a chance to look at those Poneglyphs and maybe even solve a big piece of the True History puzzle.
Conclusion
So Oda has written in three ways for the SHs (and us) to learn the name of the Ancient Kingdom during Wano: Through Zunesha, through Toki mostly by way of Oden's logbook and the Poneglyphs on Wano when Robin gets a chance to read them. The last one is especially important since based on how Luffy behaved on Sabaody, I don't know if he'd want to learn anything from Zunesha or Oden's logbook. If the SHs find out the name of the Ancient Kingdom in Wano, then it will be once Robin gets a chance to look at those Poneglyphs.....