It's completely anonymous and available on many ticket machines. There are some half-wrong info that you have to fill in a form, but that's only for commuter passes and registered cards.

You just tap Buy Suica and insert two 1000 yen bills. The system keeps 500 yen as a deposit, which is refunded when you return the card, but it's also $3.50 for a little memorabilia.

If you absolutely don't want the keepsake, you can create a virtual card from Wallet on iPhone(7 or later). I believe an app is not needed through that path. Those can be loaded from your credit card, or at pink ticket vendors with the cavity for devices(IIRC the latter didn't work initially).