The name is from Vlad, who lived before Bathory, but most of the modern day popular folklore (Bram Stoker primarily) seems to be based around Bathory. Vlad was a little weird who liked to impale enemies, but he was also a hero. The mannerisms, attitude and general habits of Dracula are much more in line with how Bathory acted.
If anything the modern day legends are at least half Bathory half Vlad inspired. I personally believe it's more Bathory but eh, lots of debates on that subject
