The name of the ship was "The Blarney Cock". It was played by the vessel "The Golden Hinde". Both received actual billing in the credits. The vessel is a replica of the real famous ship of the same name commanded by Sir Francis Drake from 1577 to 1580 on his voyages of explorations of pirating in the new world.
According to the documentary "A Pirate Ship Sails Again! The Making of Swashbuckler", this picture is the first pirate film to make use of an actual recently constructed 16th Century warship complete with cannons. The ship, a replica of Sir Francis Drake's "The Golden Hinde", was built and first launched in Devon in 1973, just a few years before this film was made.
The picture was produced by Universal Studios which was the same studio which made Jaws (1975) which also top-billed actor Robert Shaw. According to Time Out, "The success of Jaws (1975) sent Hollywood scurrying for movie adventure styles to refurbish; hence this multi-million dollar pirate swash-buckler".
The film featured two actors who had played villains in the James Bond film franchise. Geoffrey Holder had played Baron Samedi in Live and Let Die (1973) whilst Robert Shaw had been Red Grant in From Russia with Love (1963). Ironically, Shaw's character in 'Swashbuckler' was similarly named to his Bond villain, it being the fictional "Red" Ned Lynch.
The film's "Swashbuckler" title is a reference to two things. First, it refers to a genre of films of which this movie is one. Wikipedia states Swashbuckler films are an "action-adventure sub-genre often characterized by sword-fighting and adventurous heroic characters, often set in Western Europe in the period between the late Renaissance and the Age of Reason with appropriately lavish costumes". Second, the term reflects sword wielding characters. Wikipedia says that "Swashbuckler (a.k.a. swasher) is a term that emerged in the 16th century and has been used for rough, noisy and boastful swordsmen ever since. A possible explanation for this term is that it derives from a fighting style using a side-sword with a buckler in the off-hand, which was applied with much "swashing and making a noise on the buckler"."
Released in 1976, Swashbuckler (1976) was the first of back-to-back sea films for actor Robert Shaw whose next picture would be The Deep (1977) in 1977, these being two of the final films of Shaw. Moreover, Shaw starred in sea movies in three consecutive years, the first having been in Jaws (1975) in 1975.
The film's opening prologue states: "Once upon a time, some colonial outposts of Europe's great powers were ruled by villainous governors who stole the freedom and wealth which rightfully belonged to the people. Such was the tragic condition in Jamaica in seventeen eighteen under the cruelty of the acting governor, Lord Durant. The dungeons of his dark stone fortress cried with the voices of those who stood in his way. At the time, adventurous pirates sailed the waters of the Caribbean. Often, they were enemies of the tyrants and heroes of the people. Captain Ned Lynch was one of the most famous of these Swashbucklers...".