Who becomes the product owner?

Question

A business has five requirements streams, with a "stream leader" (called Product Manager, but this is an in-house term) per-stream and a backlog per-stream.

If we wanted to follow Scrum more closely, as I understand it, best practise would dictate the identification of a single product owner managing a single backlog containing requirements from all five streams (it's all just stuff to be done, right?), from which work is pulled by a self-organizing development team.

Can anyone lend any insight into how best identify the person to be the product owner and how best to explain and "sell" the modified approach to the existing stream leaders?

NB: I realize this is a very difficult question.