Ash here from the Shopify team. Welcome to the Shopify Community!
It's definitely possible to accept donations from customers on Shopify. There are a number of applications in the Shopify App Store that can accommodate this feature, but options for allowing customers to enter a custom donation amount are a little more limited. With that being said, here are some applications I found that allow customers to enter custom donation amounts:
Another option you could consider aside from an application is to hire a Shopify Expert. Shopify Experts are trusted, third-party agencies and freelancers who are available for hire by Shopify merchants to perform customizations, as well as other tasks. It's possible that a Shopify Expert would be able to create a custom solution for your shop so that customers can enter a custom donation amount to their order. You can submit a job request directly from their web page here, and an Expert will reach out to you with a quote.
It's awesome to hear that you want to work with your customers to make some sort of donations. What organization(s) are you interested in donating to?