If you intend to modify the basic top menu item, please take a look at LeftPanelTopMenuModule schema. It is responsible for menu items and methods, which regulate visibility and click handling.
Particularly, you would be interested in getTopMenuConfig method, which returns a collection of menu items. Among others, you can find StartProcessMenu item. You can override its visibility property to set it to your role, or bind it to the custom method.
Same goes for the "Home" drop down - MainMenu item in the LeftPanelTopMenuModule schema.