Starman (Danny Blane)
This one makes my head hurt.
The Danny Blane Starman is a member of the Justice Society of America. He suffers from borderline schizophrenia, and is activly seeking help for his condition. But his real name isn't Danny Blane - it's Thom Kallor.
Thom Kallor is from the 31st century, where he's known as Star Boy, a member of the Legion of Super-Heroes. Thom was sent back to the 20th century on a secret mission, but the trip went wrong. He ended up stranded on a parallel Earth (the "Kingdom Come" Earth) where he mental state deteriorated. Somehow he was able to make it to our Earth, with fractured memories of his past and a child-like innocence.
That's an awful lot of back story for one character. It tends to leave both Danny and readers confused about his past.