It's not possible to change the "StoreName" of your http://StoreName.myshopify.com address.

Don't worry though, most shops don't even use their myshopify.com address. They make their own custom domain like iloveshopify.com. Makes your shop look more professional and independent :)

No one will see the myshopify.com URL if you get a custom domain. Not even yourself (unless you go digging in your DNS & domain tab).

You can get a domain two different ways:
1. Shopify domains (we take care of the whole set up so it's super easy): 
2. Register a domain with any other domain provider and follow these steps.

If you already have a custom domain, read this: Can I use a domain that I own with my Shopify store?