What is the name of the ships designed to transport and launch various amphibious craft and vehicles along with crew and troops?

The correct name for ships designed to transport and launch various amphibious craft and vehicles, alongside crew and troops, is "Dock Landing Ships." These vessels are specifically built to support operational capabilities in amphibious warfare, allowing them to carry a variety of landing craft and troop transport helicopters. They can launch and recover amphibious vehicles directly from their decks while at sea, making them essential for executing amphibious assaults.

Other types of ships mentioned, like Amphibious Assault Ships and Transport Dock Ships, serve related but distinct roles in amphibious operations. Amphibious Assault Ships provide a platform for launching direct assaults with troops and equipment but typically focus more on aviation operations with a heavier emphasis on aircraft capabilities. Transport Dock Ships, on the other hand, are designed primarily to transport troops and equipment, which may include landing craft, but do not have the same operational flexibility specifically geared towards amphibious launches as Dock Landing Ships.

Therefore, the specificity of Dock Landing Ships to support the direct transportation and launching of amphibious craft and vehicles makes it the correct answer.