So I'm guessing you're more worried about being anonymous to the person you're paying and not anonymous throughout the entire transaction?

Patreon's FAQ about trying to have some anonymity with regards to the person you're trying to get money to. Relevant part from Patreon's FAQ.

What account details do my creators have access to?

When you are a patron of a creator, we provide the following information to them:

Your username (also displayed for anyone who lands on your profile) Email address Membership level

From a quick googlin' Bandcamp might only show the email address you've attached to your bandcamp account. Haven't gone through all the nooks and crannies of BandCamp's help pages too closely but here is there Privacy Policy that I'm skimming.

Here's a section about what they provide to the Artist, italics are mine:

Bands: When you use certain functionality or services, we may provide certain Personal Data to bands, such as your email address, country of residence and zip/postal code ("Fan Information"), and you can opt-in to be added to the relevant band’s mailing list. Bands are only authorized by us to use the Fan Information to send email to you and may not share, rent, or sell the information with others for any other purpose.