At present the notification from Stripe doesn't contain any user information so if there are multiple transactions of the same amount it's difficult to see which users have paid - other than going through each record, which the client doesn't want to do.
That email is sent by Stripe, not by CBSubs, and CBSubs has no influence in its content.
CBSubs transmits Description with user and item information to Stripe. But Description is not included in their notification mails to the vendor.
Maybe you can ask them how to add it, or suggest to Stripe to add Description to their emails (they are usually quite open to suggestions).
Sure it would be awesome if Stripe would add Description field in their notification emails, but I don't see any way for payment software to make Stripe add that to their notification to vendor mails.
As said, we send the description to Stripe, so it's just a matter of Stripe adding it to mails.
Asking Stripe support is free, and maybe there is a setting at Stripe to include it in mail, otherwise you can ask them to add it to feature requests at stripe. If you contact Stripe, please let us and the community here know of the status you get from Stripe.