Thanks for reaching out and welcome to the Shopify Community!
From what you have described, it sounds like you have purchased a domain on Shopify, but have noticed that your primary domain hasn't been updated to the new one - is that correct? Or maybe you have recently connected or transferred a domain into Shopify from a third-party host? Something else to keep in mind is that you should verify that your domain is showing in the Settings > Domains section and has a Connected status.
In either of the above scenarios, changing your primary domain should still be the same procedure. To change your primary domain you can follow these steps:
From your Shopify admin, go to Settings > Domains.
Click the domain that you want to make the primary domain.
Click Set as Primary.
Let me know if the above instructions work for you - feel free to come back here with your findings and we can troubleshoot further. Any sort of domain related changes such as DNS edits can take up to 48 hours to fully propagate, so if you have recently added the domain you may need to give it some time.
Besides this, how is the store coming along? Are you brand new to Shopify and just setting everything up for the first time? I would love to hear about your store and your plans for Shopify.
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