I would not like to name a human ship as they are weak, slow and insignificant to the Covenant war vessels. However, this vessel was already named back on Halo 3. It was docked it in Reach on an outer harbor section. It needed minor repairs due to an unwavering amount of battles.
This almighty vessel is a CPV-Class "Super-Heavy" Covenant Destroyer, spanning a 8,765 meters (28756 feet) from hull to starboard. In width it measures a fair 4500 meters (14763 feet). This, so to speak, was the largest Covenant Destroyer ever constructed under an Admiral's order. This particular warship was called the Phantasmic Shadow and it was one of the greatest, strongest and most respected of its kind. Its superiority in battle was outstanding and it was feared on most colonies.
The Phantasmic Shadow's construction was not out of the ordinary actually, it was constructed to lead a fleet of its own to wage war against planets and harvest them, a task never before attempted. The fellow Destroyers were considerably smaller and were miniatures to the flagship but they all had strong weaponry and strong shielding which made them of equal standing between themselves...not including the flagship.
The Shipmaster of this magnificent ship was none other than Fal 'Kai Taralumee. This choice was an unprecedented one as no-one expected this Special Operations Commander to become one of the sacred kind. He earned the honorary title of Fleetmaster after his warship was constructed. The current whereabouts of this fleet are unknown, however, it is certain that this fleet is a force not to be trifled with.
It is thought that this warship can hold well over five thousand warriors. Among this amount there is technicians, advisers, pilots, the Shipmaster, warriors, Unggoy and other species. Other than what has been stated, not much more is known about this vessel.