First off, to get the corresponding payment id you'd need to do two steps. The first step is to get the id of the transfer associated with the charge which is in the `transfer` property on the charge object [1]. Then, you would retrieve that transfer [2] and in the transfer object [3] you'd see the `destination_payment` property corresponding to the payment on the connected account (py_XXX).

Then, once you get this, you'd call the Update Charge API [4] using the `Stripe-Account` header [5] so that you can set the description you want on that payment.

[1] https://stripe.com/docs/api#charge_object
[2] https://stripe.com/docs/api#retrieve_transfer
[3] https://stripe.com/docs/api#transfer_object
[4] https://stripe.com/docs/api#update_charge
[5] https://stripe.com/docs/connect/authentication#authentication-via-the-stripe-account-header