The answer is yes to both.
Think about it. You guys were born and both of you inherited some identities immediately. Hindu background. Indian background. British citizenship and nationality. Male or female. Londoner. Suburban. And so on and so forth.
And as you grow, you will keep on getting new identities and discard old ones. You may move to Paris so become Parisian. You may decide to become pastafarian so ignore and drop the Hinduism. And so on and so forth. There are two lessons to learn.
One. Be supremely comfortable in what you are. Don't give a shit about what people say. You are what you are and are comfortable with it.
Two. This is more interesting. You'll realise that people love to put other people into a box. As soon as they do, then they know how to react to you. But don't allow that. Force them to create a new box for you. For example, when people ask me where I'm from, I say I'm from Burma. Or I'll say I'm from Sweden. Or talking about religion, say you're a Jedi. People get confused. And don't understand. Don't allow yourself to be pigeonholed. It's fun.
Can identity be chosen or is it inborn? – Katharine Quarmby – Aeon
Alice, the heroine of Lewis Carroll's Through the Looking‑Glass (1871), has many extraordinary encounters, but the one that's always stuck with me is her meeting with Humpty Dumpty, an egg-shaped being, balanced on a wall. He is annoyed when Alice calls him an egg, he tells her she should stop growing, and they end by arguing about the contextual meaning of the word 'glory'.
'When I use a word,' Humpty says, in rather a scornful tone, 'it means just what I choose it to mean – neither more nor less.'
'The question is,' said Alice, 'whether you can make words mean so many different things.'
'The question is,' said Humpty, 'which is to be master – that's all.'
As Alice walks away, Humpty Dumpty comes crashing to the ground.