The reporter and assignee fields are for one user. If the dropdown you are referring to is the list of possible assignees and reporters it is all the user that can create issues in the project and be assigned issues in the project. You need to remove users from access to those functions to remove them from the list.
If you are a project admin you can assign people to roles and the JIRA admin should document what roles have what permissions.
here is a link to managing permission. Copy/paste the link https://confluence.atlassian.com/adminjiracloud/managing-project-permissions-776636362.html
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