Yumi2004

I also think that she'll keep the name of Stone
As you said garooob, she doesn't like the idea that she's Hopper's daughter and I think that there'll be a problem with the school if she changes her name for no reasons

Aelita didn't like the fact she is Franz's daughter while she believed Franz was a mad scientist. Since she recovered her memories, she knows he is a good man. Besides, even if Jérémie was able to cheat the administration of Kadic, it's not easy to live with a false identity (even for a basic medical test in Tip-Top Shape), it's much more easy to use her true one. Therefore I think she will become Aelita Hopper again.