Does the app vendor obtain your name upon In-App subscription? Does the app vendor gain access to your name upon doing an In-App subscription? 

I’m not sure how to read Apple’s privacy pages to understand what information (if any) is transmitted to third party developers from Apple Account details when you enter into a monthly subscription through the iOS App Store?
The app vendor does not gain access to your name when doing an in-app subscription. No personal information at all is transmitted to them in the process of buying in-app subscriptions (nor during the initial app purchase). This is contrary to how the Google Play store works.