Yes, a user the uses JIRA Service Desk to submit a request must be included in the license and your JIRA and JIRA Service Desk licenses must match.
Alternatively you could tie JIRA Service Desk into an email account that non-licensed users could send a message to create issues.
See the first comment on https://blogs.atlassian.com/2013/10/introducing-jira-service-desk/ for more information.
As Jeff mentioned above, email import is one way to do this. We have a fictional "External user" account that is designated the reporter if the email handler can't find a corresponding user account for the email. A couple of other options would be to use an issue collector on a website, or just using a form on a web-app that uses the API to create an issue on behalf of a fictional "Form user". You could then collect their username and store it in a custom field, etc.
...be more productive while being fun to use at the same time. For some, getting started can be a bit intimidating. This is especially true if Jira Service Desk is your first exposure to Atlassian...
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG
You're one step closer to meeting fellow Atlassian users at your local meet up. Learn more about AUGs