In my cover letter, how many faculty member should I list as people I want to work with?
At least in mathematics, I would recommend something like:

"I am especially interested in working with X, as her research in Y overlaps with my interests in Z and W. I would also look forward to interacting with V and U, as their work is also related to my interests in T."

This might be different in fields where mentorship is less fluid (e.g., the laboratory sciences, if you would choose one faculty member's lab to work in).

Indeed, in my own postdoc, I learned a great deal from my formal mentor -- and I also learned a lot from his colleagues in his research group.