Currently, if a user has only permission to view a specific Subproject, but not its parent project, it may lead to confusion when using the Project Jump menu.

Consider this:

Project A
  » Content
Project B
  » Content

So, if a user has only access to the "Content" subprojects, but not their parents, they will see two "Content" entries in the menu. Also, when inside the project they can't easily determine if they're in "Project A » Content" or in "Project B » Content".
Therefore it would be good if the dropdown showed e.g.

Project A » Content
Project B » Content

but only if the user has no access to the parent project.

The H1 should also continue to show "Project A » Content", except that the "Project A" part is not linked.

Ideally, the visibility of the parent's name could be set via permissions. Thus, if a permission "view_project_parent_name" is not active, the user won't see the parent project's name, resulting in current behaviour (only subproject's name is visible).
This idea may also be extended for the whole hierarchy (all ancestors of a subproject) with a permission "view_project_hierarchy_names".