most of these answers are inaccurate - read the banner at the top of the thread that says there is no law that Abers have to try to get things right
People do seem to have odd ideas about Data Protection. [they certainly do] Put simply, an organisation can do pretty much anything it wants.....
erm no it cant really - the new thing is the GDPR - Zuckerberg thought your data was his, and the Zuck is wrong
First I think you need to consider with you daughter about what you wish to do - one letter to an old name in a few years seems acceptable - BUT if you wish to take action
then go here
https://www.scientology.org/privacy-notice.html
scroll to the very bottom
Right to Object and follow their instructions
if your daughter doesnt wish to use her own name then she could do it from one of your email addresses - using of course her old name
in answer to your question
no they are not breaking the law as they ( will say ) they have a legitimate purpose in keeping the data ....