This is not possible in JIRA out of the box as the default mail handlers cannot populate fields.
There are two addons that may help you:
Enterprise Mail Handler, it supports both Cloud and Server versions of Service Desk: https://marketplace.atlassian.com/plugins/com.javahollic.jira.jemh-ui/cloud/overview
Email This Issue (our product), which supports Server version of Service Desk as of now, and Cloud support will come very soon: https://marketplace.atlassian.com/plugins/com.metainf.jira.plugin.emailissue/server/overview
If you are a Cloud user, go with Enterprise Mail Handler now, if a Server user, I recommend you evaluate both.
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