Show sub-domain not IP

We have our domain, bgreenlifestyle.com, hosted with Dreamhost. We have our e-commerce store hosted with Network Solutions. We've setup a sub-domain on Dreamhost, shop.bgreenlifestyle.com, to direct to our store at Network Solutions.

We set this up as a re-direct, with our IP address that we received from Network Solutions. However, when you type in that address, shop.bgreenlifestyle.com, in the web browser, it displays the IP address.

How do we set this up to always show our shop.bgreenlifestyle.com sub-domain? I'm pretty sure this is possible without using the "cloak" function.