I recently purchased a bespoke domain through the Shopify domain service. This all went through okay and I received an email confirming payment.
I noticed my domain hadn’t changed and that the domain purchase was refunded to me. When I went to search for the same domain name it now says it’s no longer available.
In this situation I would recommend reaching out to our live support team to review the domain purchase and why it was refunded to you.
Once they authenticate your account they can look into any possible error messages as well as the current state of the domain and if it is available for repurchase.
To contact our live support please follow this link: Shopify Help Center - Contact Support, sign into your store account, search for your issue and use the contact support button at the bottom of the search results to see all our live support options.