What's more important to you? Tradition, identity, freedom? Maybe all of it?
Traditionally Hmong men do not change their names nor do the women legally change their names, however I imagine the whole legally changing your name thing is new to us and could represent the marriage into a clan.
There's a history behind the whole hyphenated last name bit and the same with changing last names. You can Google this later, but at the least it seems though you're okay with introducing other traditions into the Hmong culture. It's already happening anyways, amirite? If that's the case than have a blast. It seems you're more focused on identity.
Well, that's my guess anyways but I'm not the one with an online degree Hmong Culture.