Is it? My thinking was that if a name is just a name, then why place so much particular emphasis on the name of "Oden" instead of the name of "Yamato"?
My gut reaction is to say she might associate the name "Yamato" with entrapment, yet at the same time she didn't have the heart to entirely discard the name in favor of just being "Oden", which she associates with freedom.
She wants to live like Oden, yet she also uses Thunder Bagua, even though Oden never used Thunder Bagua.
She uses a club like Kaido, even though Oden never used a club.
She calls herself Kaido's son, even though Oden isn't Kaido's son.
It's quite the conflict, prob because she feels conflicted, as if she's more confident with "Oden" than "Yamato", but isn't confident enough to leave "Yamato" behind.
So this is what I've concluded: Yamato is lacking in self-worth. A character like that is the sort of character who's motivated by worthlessness, so she uses someone else's reputable name as a way to feel more worth, as opposed to her original name.