Blagar (code-name Marsopa)
and
Barbara J (code-name Barracuda)

The fleet, cryptically labelled the "Cuban Expeditionary Force" (CEF), included five 2,400-ton (empty weight) freighter ships chartered by the CIA from the Garcia Line and outfitted with anti-aircraft guns. Four of the freighters,
Houston (code name Aguja),
Río Escondido (code name Balena),
Caribe (code name Sardina), and
Atlántico (code-name Tiburon),
were planned to transport about 1,400 troops in seven battalions of troops and armaments near to the invasion beaches. The fifth freighter,
Lake Charles,
was loaded with follow-up supplies and some Operation 40 infiltration personnel. The freighters sailed under Liberian ensigns. Accompanying them were two LCIs (Landing Craft Infantry) "purchased" from Zapata Corporation then outfitted with heavy armament at Key West, then exercises and training at Vieques Island. The LCIs were
Blagar (code-name Marsopa) and
Barbara J (code-name Barracuda),
sailing under Nicaraguan ensigns. The CEF ships were individually escorted (outside visual range) to Point Zulu by US Navy destroyers
USS Bache,
USS Beale,
USS Conway,
USS Cony,
USS Eaton,
USS Murray,
USS Waller.
A task force had already assembled off the Cayman Islands, including aircraft carrier USS Essex with task force commander John A. Clark (Admiral) onboard, helicopter assault carrier
USS Boxer,
destroyers USS Hank,
USS John W. Weeks,
USS Purdy,
USS Wren,
and submarines
USS Cobbler and
USS Threadfin.
Command and control ship
USS Northampton and carrier
USS Shangri-La
were also reportedly active in the Caribbean at the time.
USS San Marcos
was a Landing Ship Dock that carried three LCUs (Landing Craft Utility) and four LCVPs (Landing Craft, Vehicles, Personnel). At Point Zulu, the seven CEF ships sailed north without the USN escorts, except for San Marcos that continued until the seven landing craft were unloaded when just outside the 5 km (3mi) Cuban territorial limit

Brigade 2506 landing fleet, which was composed of five older freighters bought or chartered from the Garcia Steamship Lines, bearing the names of Houston, Rio Esondido, Caribe, Atlantic, and Lake Charles. In addition to these vessels, which were outfitted as transport ships, there were two somewhat better armed fire support ships, the Blagar and the Barbara. (In some sources Barbara J.) 8 The Barbara was originally an LCI (Landing Craft Infantry) of earlier vintage. Our attention is attracted at once to the Barbara and the Houston, in the first case because we have seen George Bush's habit of naming his combat aircraft after his wife, and, in the second case, because Bush was at this time a resident, booster, and Republican activist of Houston, Texas.

This is one complicated operation with many players. I'll try to be brief and only answer about boats and ships. Cuban civilians, the CIA and the Navy were clearly involved, but reports vary wildly.

You asked for "military boats". FYI.....sailors only like military folks to call it a boat......they want civilians to call it a ship although we talk about "the boat". Just a fun fact. While I servedm I got yelled at a few times for that until I served aboard the USS Canopus....then I could call it "the boat" if I wanted.

First we have Brigade 2506, part of Operation Zapata, using the Maropa as the command ship. There were five old freighters bought and/or chartered from the Garcia Steamship Lines, with were named Houston, Rio Esondido (which were the supply boats and were sunk), Caribe, Atlantic, and Lake Charles.
They added some outfitted to be used as transport ships

Two were better armed fire support ships, the Blagar and the Barbara. (This one was sometimes called the Barbare J after Bush's wife). I am not sure where the Maropa was consigned from but it too was sunk. These ships appear to be manned mostly by civilians.

So our military ships "assigned" seem to be:

..........The Blagar a LCI vessel
..........The Barbara had been an older LCI (Landing Craft Infantry) vessel.
............The USS San Marcos were made to carry LCIs and is called a LCU (Landing Craft Utility) LCVp(Landing Craft Vehivle, Personnel) because they have the Landing Ship Docks built in.
...........The US Navy Aircraft Carrier USS Essex
..........The US Navy vessels, the USS Hank.USS WREN and USS Purdy
...........The US Helicopter Assault Carrier the USS Boxer
..........The US Navy Destroyers, USS Bache, USS Waller, USS Conway,USS Beale, USS Eaton, USS Murray, USS Cony
...........The submarines assigned were the USS Cobbler and Threadlin

I remember that the San Marcos and the Hank went and saw sites about their survivors.....

............So.....I found many more than Cuban manned should be the Barbara. El Baire and Blagar....the US seem to be the USS San Marcos, USS Murray, USS Murray and the USS Hank that actually were actively involved.

Houston, Río Escondido, Caribe, and Atlántico (transport ships) led by the Blagar and Barbara J (CIA LCIs).

USS Essex: Combat air patrols were flown out from this carrier.
USS Eaton (code-named Santiago) and USS Murray (code-named Tampico): evacuated retreating Brigade soldiers

Im sorry this is all I know off the top of my head. Im sure wikipedia can fill in the rest. I think there were two more ships that joined the Eaton and Murray on the 19th of April along with a submarine and another carrier much like the Essex ( USS Shagri-La).

It's documented that three boats were used in the Bay of Pigs operation. One would assume that the CIA agent who coordinated that invasion would be the one who named the boats:

- The "Houston" - named after Bush's adopted home town
- The "Zapata" - named after his company, Zapata Oil
- The "Barbara" - uhhh, do I need to explain that one?

USS Eaton and USS Murray were the first two, then later came USS Conway and USS Cony, plus USS Threadfin (submarine).

Blagar and Barbara J