I am unmarried and have a 2 1/12 yr. old child. At the time of the birth I did not include Fathers name on the Birth Certificate. I now wish to change this. What would be the best way to go about having a new Birth Certificate issued in the State of Pennsylvania to include Fathers Name as well as attaching Fathers last name to Child?

You need to do that through the vital statistics bureau in the county they were born.

***Health: Vital Records - Table of Contents
1-877-Pa-health

Does the father know that your doing this ? From the sounds of it yor wanting a name change and that may take an order of the court to get done. So long as both parents agree then it shouldn't be a problem.

And many states make you pay support even when proven your not the father

Pennsylvania being one of them.