No. Kaname is the ancient Kuran ancestor, that was brought back to life by Yuuki's uncle Rido... Before Yuuki was ever born, her biological parents, Juri and Haruka, had a son and also named him Kaname. Upon his birth, Rido sacrificed his life to bring the ancestor Kaname back to life, in the hopes of gaining power. But they fought, and Kaname's only way to retain his life was to degenerate into a baby. Juri and Haruka raised the ancestor Kaname as their own son, and eventually gave birth to Yuuki in order for Kaname to have a future fiance. So they weren't really siblings, but Kaname is not her father. And eventually Yuuki and Kaname have a daughter named Ai.
Also, yes almost a century after Kaname sacrifices himself and is put in an ice coffin, Yuuki allows herself to be with Zero. After another thousand years when Zero dies, Yuuki goes back to Kaname, and sacrifices her life so that Kaname is able to live once as a human.
Woah so much twist and turns
Thanks for your explanations
Hi guys I just skipp d through cus there's so many chapters I loved the anime so I just thought to read the end bit cus they didn't add the end apparently in the anime all the skipping got me confused so does
Zero ends up with Yuki and the biological father of Yuki is Kaname how did that happen?