Yamato

Oda has not announced in any official documentation that Yamato is Trans. We have only recieved confirmation that Yamato was born female. As for how they identify that has been left unanswered. 

Yamato wears clothing very similar to a Miko's traditional outfit, they also show no apparent shame or discomfort for their body. If anything it seems more apparent that they see no real difference between physical genders. 

It was very clear that Kaido was never pleased with Yamato's obsession with Oden. Due to this, I don't see how he would begin calling Yamato his Son after Oden's death. I believe that Kaido instead had already been raising Yamato as his heir and referred to them as his Son before the pivotal event of Yamato witnessing Oden's death. 

It was only after that event took place and Yamato began referring to themselves as Kouzuki Oden that the rest of the crew stopped calling them the Oni Princess and instead referred to them as Kaido's son. 

The final and main reason for this choice is the effects that trauma has on a young child. Yamato was clearly raised in a cruel, abusive environment. They even spend an unknown amount of time imprisoned, then are chained with explosives for years while being forced to survive like a shadow in their own home. Often times shown as starving. This kind of treatment is going to have negative impacts on a young child, so witnessing Oden's death and then finding his journal and reading it with his Daimyo's became a form of escape for Yamato. I see their obsession with Oden as more of an escape method for coping with growing up in such a harsh, unloving environment. I also believe that it was this strong identification with Oden, whom they saw as a hero, that prevented Yamato from becoming just as cruel as their father.