When using Shopify Payments, there will be a standard review to verify your identity and your business. As you've created the store under your name, it would require submitting your information. Otherwise, you can reach out to our Support to have them change the name on the Shopify Payments account and have your client submit the requested documentation.
If the request goes unfulfilled, it could result in the loss of Shopify Payments for the account and would require using a third-party payment provider which can incur transaction fees per order, which are on top of the fees the payment provider would charge you.
If you are building sites for your client(s) then they should be created through the Shopify Partner program to avoid this happening in the future.