This process will allow you to create any subdomain you would like and use it as your own branded link shortening service.
In order to do this, follow these steps:
1) Log into your domain hosting account (GoDaddy, Hostgator, Register.com, etc).
2) Navigate to DNS Settings page.
3) Add another record and configure it in following way: record type - A; hostname (or name) - your subdomain (the same you used in step 4, for example, "go" or "link"); point to (or Address/Value) - 52.21.33.16
4) Save your changes.
5) Wait for your domain to be ready. You will receive an email from Short.cm when your domain is correctly configured and DNS settings are propagated worldwide.
Keep in mind: DNS needs to be propagated all over the world in order to make the dedicated domain works. If the domain is brand new, it should take only about 15 minutes. But if the dedicated domain was registered before, it could take up to 24 hours.