You can create your own project naming structure or format in which projects are displayed in the CORE screens, drop-downs, invoices, and reports. This can be done in the Global Settings > User Interface screen, under Display As. As an example, if you want to show Project ID and Phase Name, select ROOT PROJECT ID - PHASE NAME from the Project drop-down.
You can set the format for projects as well as project phases here. Check CORE Help Center for details.