This is an accepted solution.
Cal here from Shopify, thanks for reaching out to us. I'm sorry to hear that you're having trouble purchasing a domain.
What is the MyShopify URL for your store and I'll take a quick look?
Is the card you are using attached to a bank, and is it a post-paid credit card? Have you checked with your bank why the transaction is being refused? They may be able to provide some insight here. Alternatively, I'd suggest using a different payment method to secure your domain.