This doesn't actually answer the question. The question is how to rename a subscription. The reason I'm here is because I have exactly that question.
There is nothing wrong with answering a question with "sorry, can't be done".
The answer provided, namely, that t is possible to rename the primary domain for a given subscription, is sufficient for some use cases, but not mine., We really want to keep the subscription name equal to the domain name of its primary domain. That's why I want to know how to rename a subscription (when the primary domain changes).
As far as I can see, the workaround for that is to create a new subscription with the desired name and move the domains to it.
This is not easy: there doesn't seem to be an option to copy a subscription, so its settings need to be copied manually, and in some cases (passwords), they can't be copied at all (without admin rights on the backend; we are a reseller and lack those rights). Creating a new subscription with possibly different values for properties is fine if the old subscription wasn't in use yet, but you can't just change properties when the subscription was in use.
A possible workaround for that is to have the admins enable API access and write a script to do the copying through the API, but that isn't easy either, and opening up API access is a security risk.
So at the end of the day I'm still looking for a good answer to the original question.
Reinier