The bible states the meaning of Jesus' words on the cross. Why then did some people take it as calling for Elijah?
Jesus exact words were "Eli, Eli, lama sabacthani." (Matt 27:46)
Eli-jah (literally YHWH - jah is God (El) of mine (i)) would be shortened as "Eli". Since they are the same word, in the bustle of a crowd, it is not at all unlikely that this "prophet" would be thought to be calling Elijah.
Remember, just because the words were in Psalm 22, doesn't mean the mean the people would have been assuming Jesus' first thought would be to quote a Scripture.
Pronounced "A-Lee" it sounds like a short name for "A-Lai-yah"