Ash here from the Shopify team. Welcome to the Shopify Community!
I'm sorry to hear you're having issues purchasing a domain through Shopify. I'm happy to help out with this! To help me understand the problem in full, could you please send me a screenshot of the error you're receiving? Additionally, I have some steps I'd like you to try. After completing these steps, please go ahead and try purchasing the domain again, and then reply back here and let me know the results. Here are the steps:
I hope this helps, and I look forward to hearing back with your results.