Although you could say this is the “ultimate level” for Cassandra anyways, the name is supported specifically by this panel, in which Cassandra admits her hopes for the future to Tim Drake:

Because Batman: East takes place in a universe where Bruce has died (“done”), it makes sense for Cass to seek out this mantle to  memorialize him. Yes, Dick has become Batman in this universe, but as we have seen from the Batman, Incorporated, comics run, this is merely a title rather than any one person. The “:East” portion signifies Cass’ dedication to the continent of Asia, not only connecting with her racial roots but providing strength, protection, and leadership to an area of the world often ignored by the DC Comics world unless it is to fill in a convenient stereotype, such as ninja or martial arts training. As an advanced member of the Batfamily proper and daughter of Bruce Wayne, it stands to reason that she would be the point of coordination for lesser known heroes such as Jiro Osamu. 

That being said, I know many people will still challenge this seeing as though Cass wore the “Batgirl” title for years. One of the major goals of Batman: East is to challenge its audience’s assumptions about identity and what that means. For instance, while the “Robin” title was for generations associated strongly with males,  characters like Carrie Kelly, Stephanie Brown, and now Helena Wayne have helped to transform the concept into a gender-neutral synonym for sidekick. [omitted due to spoilers; will be revealed later]. 

Batman: East also challenges the concept of “Batman” by including a meta-human (and a powerful one at that) beneath the “Batfamily” moniker, proving that the Batman mythos is more deeply rooted in the power of overcoming struggles such as  insecurity and fear by sheer dedication and perseverance rather than being a simple “no powers” vs “powers” argument.