Currently it is not possible to use create a subdomain, f.e support.example.com and link this subdomain to the service desk url https://www.example.com/jira/servicedesk/customer/key.
Use a Reverse Proxy or URL redirect service external from JIRA.
Another workaround is described in How to customize customer portal URL in JIRA Service Desk Server
- Please ensure you test this first on your test instance before you implement on your production.
- Please also note that Atlassian does not support this customization.