Only with traded Pokémon that lack a nickname. Per the SwSh website, "if a Pokémon you received in a trade doesn’t have a nickname, you’ll now have the chance to give it a nickname—but only once!"
That makes sense. I guess they didn't, couldn't, or forgot to code a distinction between a...
But Ash-Greninja is a super-special-anime-tie-in form while GMax isn’t as special. And plus, there’s something called Dynamax power right? Maybe that could factor into the ability to GMax and be passed down.
You said capturing a pre-evo Pokemon and leveling it up and evolving it is a hindrance if its final evolution is available, before, in a later post, stating that exact thing is lazy. If its a hindrance, then it would be more work, hence the contradiction.
Is it? I figure getting a Pokemon at a (presumably) lower level as a pre-evo is more advantageous than capturing its high level final evolution. By the time the pre-evo evolves, it will already have some EVs and friendship while a final evo just caught has neither. Pre-evos can also learn...
While nothing has been confirmed, I don't think this will be the case. GameFreak wants to make obtaining competitive Pokemon much easier this generation; preventing Pokemon from passing down their GMax ability seems counterproductive to this end.