I have this card as well. It's much better than a residence permit and yes it allows you to do many things under your Chinese name on the card including opening a bank account but it's always more of a hassle than using your actual name so it is not really worth it to use the Chinese name unless you really have a strong desire to do so. Booking air tickets under your Chinese name is no issue but you may have a problem getting points from your preferred frequent flyer program as the names won't match. You won't have a problem getting through airport security and the automatic domestic departure security check in certain airports like Hongqiao and Shenzhen will work for you. You'll now be able to take the train using your card as the ID, makes it a bit easier than scanning your passport but you need to make sure you're registered under the train app using your card not your passport.

I used BOC when opening up my account with the card, they knew what they were doing (at least at the branch I went to) and now I can transfer 50K USD a year into and out of China no questions asked just by doing it on the BOC app, no bank visit needed. Go re-register yourself with the police in your community using the card as your document, then change phone, bank, etc to the card if you wish.

The main benefits of the card remain unlimited stay in China without a visa and no need for a work permit for a job you want to do. All the other stuff is kind of neat, but not much different than using a passport.