Kaname is not her real brother. He was rased by Yuuki's parents but was not their real son. He was one of the 1st vampires to ever roam the Earth. Then somewhere down the line, he couldn't suvive as a vampire, so Yuuki's parents sis that they did with Yuuki (sort of), they made him human. But then Rido, Yuuki's uncle, tried to eat Kaname, he regained his true vampire form and soon after that, Yuuki was born and he continued to stay at their house, not only because Kaname owed Yuuki's parents his life, but because he had also feel in love with Yuuki and wanted to protect her. So no, Kaname is not Yuuki's real brother.
ps: this is not in the anime. the anime does not go that far into the Vampire Knight story yet. This is all explained in the manga.
Hope this helped!! XD
Vampire Knight (the manga)