It's an issue view screen.
Go to the project admin and look for the "issue type screen scheme" - descend into that until you find the screen scheme for the issue type you are looking at, and then go into that to see what fields are defined for viewing.
For customisation, all you can do natively is re-arrange the order of fields. Note that JIRA ignores some fields in there and re-arranges them for you. System fields always appear in the details section, attachments gets its own section, all people type fields are grouped and so are dates and times.
If you want to customise it more than just ordering fields, you'll need to start hacking core code (not advisable), although using add-ons to add tabs or custom field types that do different things are not a problem.
How do I move Reporter above Assignee, so the displayed order is consistent with all my other screens?
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The Jira issue view is not configurable that way - you'd have to hack some code to do it.
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If you're on Cloud you can use https://marketplace.atlassian.com/plugins/customizer-jira/cloud/overview to customize it.
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