momo already hid his name, that was a bad writing decision from oda imo, and could just not put emphasis on it, remember the flashback that kin'emon had when kaido was about to kill him, and how they were training to pretend that they're father and sone, that's not proudly carrying the name, it's cowedice and shows that everything was handled by the scabbards.
well kaido had people all over the new world looking for the scabbards since kanjuro was actively feeding them information. it is better to do that at that time for safety reasons when they were targeted by such powerful people.
he literally lives in a high castle, the fear of heights suddenly appeared out of no where, are you suggesting that kaido holding him in that manner was the trigger for that? because i don't think so, momo words means that he always had that fear.
here are the panels :
chapter 701 - when luffy suggests that momo should fly
chapter 973 - when kaido asks momo "what is your name?"
it was made pretty clear in the story that his fear came from kaido holding him up like that. and its going to wonderfully tie in with him carrying luffy up to the rooftop by flying and therefore breaking that fear.
what's that suppose to mean? the important thing is overcoming the defeat momo is still crying to this day.he overcame nothing despite the fact that it's been months since his family's ruin.
crying isnt wrong lol. he is an 8 year old what do you expect? he's been through a hell of a lot and the only moment he cried in onigashima was when - 1. he almost died. 2. kiku and kinemon died. how is that a bad thing???
the journey was decided by the scabbards and toki, he was basically just a figure head, and the udon moment proved that, he never felt the weight of responsibility until it was throw at him there. he himself knows that the people only see oden not him, and even hyogoro talked about him as just a symbol of hope towardst the future, when the ignition of their moral was supposed to be entirely from luffy.
but he did go on the journey. he was shielded from everything by oden (obviously because he's just an 8 year old kid) and was thrown into the limelight suddenly. he's now slowly understanding his importance, his role and his dream. this whole story arc from punk hazard to wano is momonosuke's tragic backstory and redemption arc. and yes, he was mainly inspired by luffy.