There is technically nothing preventing the input of a name that's not real (some people have clearly done it), but at the same time I can't advise doing it as that may cause some trouble. On our end, the name information is not shown for payments made to itch through PayPal so maybe in that case it's not a required field, I'm not sure.
Direct transfer via PayPal or bank account for donations is not something we are planning on doing. If you understandably are cautious with your name, you'll understand that putting an IBAN online is not something we want to go for. These options are also not good for accounting, which is important if meaningful amounts of money are donated to support the project.
Right now the only option we offer is to donate via Itch (using the payment methods supported by Itch), however we'd like to also set up a way for people to make recurring donations if they wish to. There are many potential different services that could be used to collect donations, we haven't yet studied them to decide which would be most suited for our goals.
If people reading this thread have some experience with different services that can be used to collect money for a project/goal, let us know.