You can customize your receipts to include your custom logo https://dashboard.stripe.com/account/branding …, and additional information here: https://dashboard.stripe.com/account/emails however, the legal business name will still appear on the receipt.
Gotcha. You can't customize that right now with Stripe's out-of-the-box receipts, but you could look into rolling your own custom receipts: https://stripe.com/docs/recipes/sending-custom-email-receipts …).