Board Thread:Anime/@comment-36552187-20180913104607/@comment-1327106-20181004040241

Levi tells Kenny "My last name seems to be Ackermann, too," which suggests that it's something he heard rather than knew. He wouldn't use "seems" otherwise.

Also, when he first meets Kenny he says his name is "just Levi" and from Kenny's reaction we see he understands why Kuchel didn't give the Ackermann name to her son. These two lines together heavily suggest that Levi didn't know he was an Ackermann until the Interior MP mentioned Kenny's last name, and even then, only because he suspected that Kenny was his father.

It's less clear in the anime, but in the manga, you can see a mix of surprise and disappointment on his face at learning Kenny is actually his uncle.