To the best of my knowledge, the only way to do this would be if you were a Service Desk Agent, or Project Admin with agent access. You could then still do this in the customer portal when creating the request, or via the Jira main web portal by the method Edwin recommended.
But otherwise, I don't see a way for other (non-agent) users to be able to do this. In that case, I would recommend just adding a text comment to the issue that is created to explain to the Agent who this request is really for and ask the Agent to change the reporter value to the username/email in question.
...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...
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