I see "empire building" as a larger campaign. In some cases, vanity hiring is really just vanity hiring, motivated by noting more than the impulse not to let your peer's headcount pull significantly ahead of your own.
I think you could argue it already has a more general name; individual self interest. The peak headcount you’ve managed or directred has a pretty direct impact on the level of manigeiral roles you are in contention for.
It already has a name; empire building