It seems entirely natural to do this. What should you do instead?

With stripe, the testing environment is sufficiently powerful that you don't need to test in production. With the test environment, you should have enough confidence that the integration will work. If you feel the need to do a payment after going live, ask a friend to do it, not someone from your household.

HTF does stripe know you from Adam?

Or do they just ban the card used to make the first payment on every integration (while ringing a bell and high fiving each other)?

Stripe knows your name, which you had to submit to go live. If your first payment is with a credit card in your name, particularly if it's a large amount (which the fraud system flags as money laundering), you will get banned with 100% certainty. Ask a friend who doesn't share your last name.