Ryder here, from the Social Care Team at Shopify. Welcome to the Community, and thanks for posting! Domains are considered non-tangible, irrevocable digital goods which are not exchangeable or transferrable. Once a domain is purchased, it belongs to the buyer for the year ahead and cannot be refunded or exchanged. This is outlined in the ‘Domain Registration Agreement’, which is presented at the time of domain purchase.
What I can recommend doing moving forward is disabling the automatic domain renewal for this domain. This can be done in your Admin by going to Online store > Domains and selecting the domain in question under Shopify-managed domains. In the Auto-renew section, you'll need to uncheck Auto-renew this domain every year.
If you decide to purchase a new domain to match your shop's new name, you can keep the old domain attached to your shop so that previous visitors and buyers can still find your website by typing in your old domain. In this case, you'll want to be sure to set your primary domain as the new domain. Also found on the Online store > Domains page of your Admin, click Change primary domain and set the new domain as the primary option. This will cause your old domain to automatically change into the new domain in the address bar once visitors arrive to your site.
Hope this helps! Please let me know if there's anything I can clarify.
Just to confirm, you followed the steps listed out in this guide and were unable to disable the domain renewal - is that right? What're you seeing in the 'Auto-renew' section of your domain page? If you're able to please share a screenshot of this section, I'd be happy to see if we can walk through it together here.
Regrettably, we don't have access to your domain. We're also unable to authenticate your account through our social channels, for security purposes. That being said, we welcome you to reach out to our Support Team through the bottom of our Help Center page by logging in and selecting your shop. One of our Support Advisors would be happy to walk you through the steps as well and can look into your account to see if anything on the back-end needs to be done.
Hope this helps!
I think it impossible. If you really want to set the domain name for your current store, you should build your new store with that domain like your current store and redirect (301 redirect ) your current store to a new one.
Hope it helps!