In order to sign up for a developer account, I'll need my parents credit card. However, after going through the signup process, my Dad's name shows up because he is the credit card holder. How can I publish an app under my name, if I don't have access to my own credit card? Should I buy a prepaid one?
Apple is a stickler for the legal name being legal and legitimate. As you're aware, you must be at least 18 years old to legally sign up for Apple's Paid Developer Program.
I've seen children who publish apps with the by line saying "By Child's Name and Parent's Name" and the seller simply being the parent. Here's an example. The child, Thomas Suarez, is 12, and he published the app like above.
I don't believe that there's any other way, besides creating a company and publishing through that. Then you'll have a company enrollment instead of a personal account. It's more work, but if you can't abide by having the legal name of the parent show in the App store, it's your only avenue other than lying and not getting caught.