If you've bought a domain from Register.com, you must reconfigure your DNS settings to point the domain at your Shopify-hosted storefront.

Set up your domain with Register.com

Make sure that you've added your custom domain by clicking Connect existing domain on the Domains page of your Shopify admin.
To set up your domain with Register.com:
Log in to your Register.com account.
In the Account Dashboard section, hover over Domains and click Manage

Click Manage in the Domain row in the table: 

In the Advanced Technical Settings section, click Edit IP Address Records

Replace the existing IP address with Shopify's IP address in the text box: 

Click Continue.
Click Continue again to confirm your changes.
On the same page, in the Advanced Technical Settings section, click Edit Domain Aliases Records

Enter www in the first text box, and enter shops.myshopify.comCopy in the points to text box.
Click Continue.
Click Continue again to confirm your changes.
Click Verify connection in your Shopify admin to confirm that your custom domain has been connected to your store.
It can take up to 48 hours for changes to take effect.

If you are unable to edit your DNS records from within your domain provider's admin section, then you must contact Register.com support .