To the extent that the blockchain might not show your name and address, yes, you can donate anonymously to nonprofits on the Better Giving marketplace. That does mean that you would not be able to request a tax receipt, and so the form to do that can be safely ignored.

However, some countries and nonprofits do require donors to complete 'know your donor' or KYD details in order for their donation to be accepted. You will not be able to donate to those nonprofits without first completing the personal details required.