User is trying to create a phased project from a project template in Core, but noticed that although the Parent Project ID copies to the phases properly, the phases still have the template's project name.
This is the expected behavior in Core. When you create a project from a template that has phases, you need to specify an ID for the parent project and Core prefixes this ID to the IDs of all the new phases being created. However, the phases retain the project names specified in the template. You can overwrite them, if needed. Check the Core Help for details.