Hi Kevin,
Unfortunately you can't directly manage what is shown in this menu - the items are contributed by either JIRA or JIRA add-ons to set the default home page for the current user and can't be changed through JIRA's admin UI.
You can contribute new items in the "MY JIRA HOME" section with an add-on with the web-item plug-in module - https://developer.atlassian.com/jiradev/jira-platform/building-jira-add-ons/jira-plugins2-overview/jira-plugin-module-types/web-item-plugin-module. The section is section="system.user.options/set_my_jira_home".
There are also some very hacky ways to inject global JS/CSS that can hide or alter the menu for all users. One such way is to use an announcement banner with <script> tags. But I wouldn't really recommend it.
You must be a registered user to add a comment. If you've already registered, sign in. Otherwise, register and sign in.