Aleka is a name River made up, a character from one of his fictional stories:

"Aleka is a poet philosopher, and the attic is a meeting place where he lives and has a secret society. People come and visit him and read his works, then he dies and they meet regularly and continue the reading of his works, and from that - learn their own, and become filled with this new passion for life, and they express it through music and form a band. We’ve put it in a fairytale setting."  - River Phoenix