You can use your own domain or subdomain as the domain name used with the COS URL shortener.
To do this, you must first go into your domain hosting, and create an "A Name" on your domain or subdomain and point to IP address 184.108.40.206
After this has propagated through the internet (usually 2-4 hours) it will be available for use.
Once ready, you can learn how to use your URL with the COS URL Shortener here.
Architecture of the COS Link Shortening System