Are Levi and Mikasa siblings? I've heard Levi being called as Levi Ackerman, which in Mikasa's backstory, you discover that her last name is Ackerman as well, although no recognition passes between them, and you never see them together as children.
No they are not siblings.
Below are some details you may not want to know if you have only seen the anime.
Levi is the son of a prostitute named Kuchel Ackerman who died while Levi was very young. His serial killer uncle, Kenny Ackerman, took care of young Levi growing up to a limited extent but obviously was not a good man. Mikasa's father was an Ackerman while Levi inherited the name from his mother's side of the family. His biological father is unknown. They, therefore, are not siblings. It should be noted that some bloodlines in this series have special abilities and the Ackerman's seem to be one of these bloodlines.
It is not clear how closely related they actually are beyond that as most of their family trees are unknown.
The spoiler below is a quote from the wiki.
When Captain Levi Ackerman speaks about Kenny Ackerman, he asks Mikasa if she was possibly related to him. Mikasa retells that when her parents were alive they told her that her father's family, the Ackerman bloodline, was persecuted inside the cities and that her Asian mother's family lost a place to live inside the cities as well, possibly because of her race. Mikasa then states that her parents met as fellow people who had been driven into the mountains and out of the cities and got married. She claims that her father never knew why the Ackermans were discriminated against and that they weren't of a different race like her mother was.