In this case though that is irrelevant. Vlad II was named Dracul because of his joining The Order of the Dragon. The naming of figures that were popularly courageous were called a Zmaj (Slavic for Dragon l has routes in Snake). In this case the two are seperate and both have no connection with the Devil. In fact The Order of the Dragon was a Christian organization. Why would they name their order and someone in their order the devil?
To be fair, the Order of the Dragon that Vlad II joined was named after the dragon from the story of St. George and the Dragon. It was modeled after a similar chivalric order called the Order of St. George. St. George was thus also the patron saint of the Order of the Dragon. The dragon that appears in that story was long associated with the devil, which can seen quite clearly in a lot of medieval artwork.
So, the Order's use of the name and imagery of the dragon is in part referencing the story of a dragonslaying saint. However, they still used an image of a dragon coiled into a circle with its tail wrapped around its neck as their badge, and sometimes called themselves the Draconists. So the imagery is a little mixed, but it does mostly make sense.
On a tangent, since you mentioned the root of Zmaj, the word 'dragon" itself comes from the Greek "drakon", which meant serpent or giant seafish. I think "drakon" literally means "fire-spitter", but that was actually a reference to the intense burning sensation caused by snake-venom rather than literal fire originally.
wasn't Vlad called Dracul, meaning Son of Dragon?
Actually, Vlad the Impaler was named Vlad III Dracula (also written as Drăculea). "Țepeș" (the Impaler) was a nickname used by either him or his enemies. Dracula was actually part of Vlad III's name. Dracula meant "son of the dragon", coming from the fact that Vlad III's father took on the name Vlad II Dracul (which just meant dragon).
The name Dracul actually led into what their entire branch of the ruling family of Wallachia was called: the House of Drăculești. Members of the House of Drăculești occasionally ruled Wallachia from 1436 to 1600, so the family name stuck around for a while. Of course, that entire period say a lot of violence, war, and assassination, with the House of Drăculești fighting for control against their rival family, the Dănești. As a piece of videogame trivia, one of the allies of Trevor Belmont was a member of the House of Dănești; they just butchered his name in translation and called him Grant DeNasty.