You will be able to find the list of all payment providers you can activate. To get these up and running you would indeed need to get in touch with each gateway independently, get the papers done with them and finally integrate with Shopify as per their guidelines.
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Shopify does not require a business trade license to operate your store, but that doesn’t mean you don’t need one for everything else. Since you seem to have all papers ready, you can get in touch with payment gateways to setup payments, they will require paperwork which you would need to provide for sure.
With Easy Pie Checkout for Shopify, a 3rd party Stripe-powered checkout solution, you can accept payments and subscriptions with many payment methods supported by your Stripe account.