If you're delving into the idea of nicknames, look at what they say about you, not just the people around you. You're capable of assimilating in a variety of situations, but which Hannah/Hans/Hannah cat is the real one? If we wear a mask for long enough, does that become our real face? Are we simply who we spend the most time being, or is there more to our multifaceted identity?
It's hard to disagree with this prompt, so you'll have to try and challenge it in a different way; namely:
why do we have different identities? I suppose you could argue that we all only have one identity, just with multiple forms/layers/'masks', but I think your current contention is probably a stronger line of argument.
In terms of the why: consider identity as a mutable or fluid concept (ever changing.) I haven't read your text, but going off the title and wikipedia alone

look at the way culture can manifest itself in different ways. Have the contributors to this book had to sacrifice/compromise elements of their cultural identities for the sake of forging a new life, or have those values simply changed into something else? Maybe they've amalgamated with Australian culture to form their own unique traditions, or perhaps they are adept at wearing different masks at different times.
Another point that may be worth exploring is the idea of a linear identity (one that goes from point A to Point B, or in this case, coming from an Asian background to an Australian culture.) Is it correct to say our identity changes from one to the other completely? Or is it more complex than that?
Not many examples here, but hopefully that sparks some ideas for you

Best of luck for your SAC!