You just need to submit some paperwork to the Pennsylvania Department of Health. I have attached a link with all of the relevant information. Take a look at the part of the page that says "How to Correct a Birth Certificate with a Court Order".
If you found this answer helpful, let me know by clicking the "Mark as Helpful" button at the bottom of this answer. This answer is provided for informational purposes only. This answer does not constitute legal advice and it does not create an attorney/client relationship. More importantly, the information contained in this answer should not be relied on as legal advice.