I wouldn't consider it as a "Famous person" but more of a "Player in a big sport". A bearer of Aleksi is in the NHL, with Aleski Heponiemi of the Florida Panthers being one that bears it.
Aleksi is also the Georgian form of Alexis. In Georgian, Aleksi is written as: ალექსი. [noted -ed]A known Georgian bearer of this name is Aleksi Aleksishvili (Lekso for short), Georgia's current minister of Finances.
Wow, I'm loving this name, I've never met anyone named Aleksi, but it sounds very cool yet refined. Great name for a man/boy, it's definitely not boring or over-used.