It makes more sense to say Dracul than Dracula.
"Dracula" means "Son of the Dragon(Demon)".
It really cheapens the phrase if he says "I am the son of the Dragon(Demon)" since he had no father figure to speak of in the game, thus no frame of reference, and would have been hilariously confusing to anyone playing it who knows of the meaning of the word. So I understand why Gabriel would say that.
"Dracul", in our world's history, is Vlad Dracula III's father, Vlad II.
"Vlad II received the surname Dracul in 1431, after being inducted into the Order of the Dragon, founded in 1410 by Sigismund, the Holy Roman Emperor, as part of a design to gain political favor for the Catholic Church and to aid in protecting Wallachia against the Ottoman Empire." -Wikipedia-
Vlad Dracula III is 'the' Dracula that's the figure that our Castlevania Dracula and Stoker's Dracula and others are based on. He would be son of Vlad II (no last name). He would be called Dracula to mean "Son of the Dragon" or "Son of one from the Order of the Dragon", but was mis-characterized due to a translation error so that "dragon" became "demon".
His other title "Tepes" literally means "The Impaler". It is not a last name, but rather a glorified nickname he was given. Thus, when people say things like "Vlad Tepes III", they're misinformed. His true name would be "Vlad Dracula III".
That's the very very loose connection between our world's and Castlevania's world's Dracula character.