Stoker did not set out to borrow a real prince's name. He was looking for a word that meant devil, and a footnote handed him one.
His working notes show that the vampire was not always Dracula. One abandoned outline had a "Count Wampyr," confronted by a German professor. The name he finally used came from William Wilkinson's history of Wallachia and Moldavia, published in 1820. Stoker copied out its note that Dracula means devil. Wilkinson added that Wallachians gave it as a surname to anyone remarkable for courage, cruelty or cunning.
Scholars long assumed Stoker read the book on holiday in Whitby in 1890. More recent work shows he could also have used it at the British Library and the London Library in London.
The name itself is older and has a more specific meaning. Sigismund of Luxemburg, King of Hungary, founded a knightly fraternity called the Order of the Dragon to resist the Ottomans. When Vlad II of Wallachia became a member, he took the byname Dracul, "the dragon." His son, Vlad III, was known as Dracula. That is a Slavonic genitive, meaning "(son) of Dracul."
Fifteenth-century sources wrote the son's name as Dracula, Dracuglia or Drakula, and he signed two letters himself as Drakulya or Dragulya in the 1470s. The devil sense comes in because modern Romanian dracul also means "the devil." Wilkinson was reporting a real double meaning.
The link between Stoker's count and the historical Vlad is weaker than films suggest. Vlad does not appear in Stoker's notes. Elizabeth Miller called the connection tenuous, noting that a writer who used so much small detail left out Vlad's notorious cruelty. Stoker seems to have wanted the meaning, not the man.
The deepest root is Latin draco, from Greek drakon, "serpent." Etymonline traces English dragon to the same source and glosses the Greek as "huge serpent." So the most famous vampire in fiction carries, at bottom, the name of a great serpent.