"Luffy not calling Yamato by her real name = Luffy not acknowledging her presence" is such a shallow argument. Correct me if i'm wrong but i don't remember Luffy calling Chopper by his name in the Drum Island Arc either.
Luffy being surprised and impressed by Yamato holding off Kaido alone for him while he was away and thanking her is more recognition and respect than Luffy has ever given Carrot, i.e ignoring Carrot when she bites his ears, or being saved from under Katakuri's boot and never asked if she was okay.
Luffy telling Yamato to protect momo shows that Luffy already treats Yamato more naturally and has more trust in her like his own crew by giving such an important job to someone his has just met, just like when Luffy tasked Franky to protect Robin in Enies Lobby when he was busy fighting Rob Lucci. Carrot actually has more recognition from Sanji, since Luffy never consoled Carrot when she was grieving Pedro's death. It's also Yamato that Luffy is fighting alongside right now against Kaido, he isn't gonna come to help Carrot in her fight against Perospero.
Luffy was already listening to Yamato's story in the attic when they first met, despite how hasty he was, and also removed her cuffs for her. It was there where Yamato also told Luffy her dreams and goals, has Carrot done that yet?
Carrot meanwhile has never had, and still hasn't had the developments and writing necessary for a straw hat, she has never been a main character in any of the arcs she's been in. And now that she's not even fighting a important member of the beast pirates, she's completely removed from Wano's central plot and story, not that she was ever important to begin with- Carrot also wasn't a main character in WCI either.
The truth of the matter is that no other character aside from Yamato in the current Wano Arc is being developed as the potential next straw hat, no other potential straw hat has their dreams and ambitions explored on the level of Yamato's.
Tama was the first possibility, but then her saying that she wants to see Momo as Shogun and live in a free Wano was the nail in the coffin imo.
The only character that's given enough focus and writing in the Wano arc right now, enough for them to be a straw is Yamato.
Yamato won't join because Luffy doesn't call her by her real name is a pretty meaningless argument imo.