To customize the URL of your Clyp, you need to be a Premium subscriber. To change the URL, go to your profile page and find the Clyp you want to customize the URL for. Click the "Edit details" button for that particular Clyp. Underneath the description input field, you will see a field to add your custom URL.
Keep in mind that whenever you create a customized URL for your Clyp, that specific URL is yours forever - no one else will be able to take it. Even if you decide to update the customized URL to something else, the old link will still work.