We want to be able to pass through the API the Shopify customer order number, eg #1067, etc to Stripe into the "description" under payment details.
Stripe said this is possible and we need Shopify to provide documentation on how to do this. Shopify said to write the question here!
To add a cherry on top, we only need/want to do this for purchases via the Recharge subscription App. Only recurring purchases go directly to Stripe, all one-time buyers stay in Shopify.
I can't find the documentation on passing trough purchase data via Shopify's API.