Use your own domain or subdomain for your StoreConnect store. Creating a Web Domain record and entering the desired domain will, generate a target field after it is saved, which can then be entered into your DNS settings as a new ALIAS record for root/apex domains or a CNAME record subdomains.
You may want two targets for the one store if you wish to make it available at your-store.com and www.your-store.com. If so, create a Web Domain record for each.
Once your Web Domain record is set to 'Active', the status field will update as the connection is established. Starting at Enqueued, the status could take 10 minutes or more to progress.
If there are any problems making the connection, the status field will change to 'Failed', the Active checkbox will be set to false, and the Message field will populate with the reason for its failure. The connection can be retried by again checking the Active checkbox and saving the record.
On successful connection the status will report 'Success'.
Make sure you update the Domain Name field within the Store record to see your site live on your own domain.
Important notes
Setting the DNS record TTL to 1 minute, or as low as your DNS host allows, initially will help speed up the process. TTL can then be set to a longer time after everything is working.
Some hosts do not support ALIAS and so you will need to configure a CNAME only and then set up forwarding from the root domain to the subdomain, or change DNS hosts.