You can be transgender and is okay if you decide not to tell everyone, it is up to each individual. In Lottie’s case ultimately the decision is hers if she wants to tell anyone at school and seems that has support of parents not to do so at her “new primary school”.
Having been the subject of bullying myself at school and bullying or harassment when came out as trans by some people in the community I can totally understand why Lottie would not want to come as trans to everyone. Changing schools as well as not identifying as trans to everyone has stopped the bullying for Lottie.
I can only imagine what her parents went through when Lottie came out to them as trans and months afterwards as they came to terms with it. A lot of society still doesn’t understand what transgender children or adults go through and how courageous it is to be your true self living as such.
Unfortunately the reality is that we still have to be cautious identifying ourselves as trans and especially with transgender children because a lot of people still lack empathy or understanding and can be quite abusive towards those of us who are trans.
The main thing here is the Lottie is happy and will be able to grow up as such without fear of abuse, bullying, or harassment because she is trans. One day hopefully most if not all of society will understand trans people so all of us can come out as trans if we wish to without fear or retribution.