This often happens when you are not passing the correct
Currency in your checkout (this is not a configuration in Magento).
For most HPP payment methods, a specific shopper country code and currency are required for the payment method to be displayed. For example, iDEAL will only show if the shopper is located in the Netherlands and the processing currency is EUR. For an overview of which countries are supported for each payment method, refer to Payment methods overview.
Another reason could be that you are using a third-party checkout module that interferes with the Adyen plugin.
The Adyen plugin should dynamically inject the HPP methods, depending on the billing address country. The injection happens in this function. Your third-party module can prevent this observer execution. To check whether this is the case, you can disable the third-party modules, and use the standard Magento checkout instead.