Vlad Tepes has always been Dracula. That is what people called him. But not because he was a vampire. Stoker popularized the IDEA of Vampires. Dracula got entangled with it, and thus an icon that represented universal vampires was created. Vlad Tepes, as he was referred, was better known among the country folk for impaling his enemies and people that stole from him. Thus, Tepes, which doesn't really mean "the impaler", but is derived from a root word that means, to impale.
Stoker heard of these stories, and other similar ones, I'm sure there was some rumors tossed in there by his enemies, and wove a fictional story about an eccentric man, possessing of all these qualities, but who also happened to be an undead being who drank of human blood. I'm not really sure why it became so popular, but somehow became associated almost universally with Vlad Tepes = Dracula = Vampires, and so on.
Just to be anal, Dracula doesn't really mean anything in Romanian. I am not sure if it did at one point, or if the language was vastly different back then, or some sort of bastardization happened, but the current day word, drac, means either devil, devilish or demon. Or something along those lines. It's more commonly associated with some sort of hellish, otherworldly forces, of the evil/mischievous variety. For example;
a-l a pucat dracii, literally, means, "devils/demons got a hold of him". It's used when someone loses their temper, or otherwise does something out of character.
I wouldn't be at all surprised if somewhere down the line, the idea that drac somehow meant dragon, was mixed in there. It makes MORE sense that it was meant in the form of the above, relating to devils or demons. It just makes more sense his enemies would call him that, than the obscure dragon, which doesn't make any sense in Romanian, and as far as I know, they have no word for. Try to look up dragon in an English-Romanian dictionary, and you'll get the literal "dragon" (borrowed from English) or other words that don't even closely resemble it.
Another example, to tell someone to go to hell,
du-te ta la dracului!, "go to the devil", obviously, "go to hell", where the devil would preside.
I know this is kind of off topic and an interjection, but it pisses me the f* off whenever someone says that drac means dragon. No, sorry, it doesn't. The best part about it, it makes more sense with the Castlevania mythos. Whether the developers were aware of this or not, well, it's pretty cool either way. Because to his enemies, Dracula was either a devil, or a symbol associated with darkness and evil.
Another example to further solidify my point,
Ce dracu vrei?, means, rudely, "what the hell do you want?"
I don't see how a dragon fits into there. At all. To be even further anal, the naming convention is borrowed from a different culture. It seems more likely to me that the name was derived from a Slavic interpretation of the name, than Romanian itself. Adding the "a" to the last name of a newborn is a common convention in Russia, for example. Well, Wallachia, very close to Russia, probably part of it at one point. Not too big of a stretch. His enemies probably referred to him as the devil, or the devilish one, or something similar. It's most probably a name that stuck, and wouldn't have been popular with the Romanian people, at least, the ones that supported him. But it makes for good fiction, so it was used by Stoker.
There seems to be a lot of mixed history, and even Wikipedia has some of the facts fudged up. The worst one I see tossed around is that Dracula means Dragon, or son of Dragon, or some other such nonsense. Whether his father was of the order of the dragon or not, is irrelevant to that fact. I think people just see the two words and automatically associated them together. Language is complicated and has changed a lot throughout history. The Greeks seem to have a word for Dragon that is close, roughly (the characters may not show up, so VERY rough interpretation) drakon. But was associated more with serpents or snakes. If we tie that back to the bible, the serpent/snake = satan. Ta da, we are back at square one. So please will you all stop saying Dracula means dragon.