The reviewers play an important role to journal. Reviewers also gives the time to review the manuscript and help to the editors to select the high quality paper. It means the Editors and Reviewers both are responsible to improve the journal quality. So the name of the reviewer should be given on the journal website.
From what I know since the time that my work underwent its first peer review until now that I am peer reviewing manuscripts, the final accountability lies with the Editor in Chief. He calls the shot in journal publication. A reviewer is like a government adviser who can suggest and recommend action but is not an executor of the advise. Your underlying question is why keep a reviewer's identity secret. While common sense dictates transparency for peer review, non disclosure of the reviewer can also promote collegial trust. The reviewer should not be prejudicial or patronizing of the work of the author, while the author should lay his/her trust fully on the review process.
The structure used by scholarly journals is called "double blind review." That means that the reviewers do not know who the authors are and the authors do not know who the reviewers are. This is to ensure that reviewers do not experience pressure to approve sub-standard articles.
Publishing the details of who the reviewers of a certain article are would violate this principal. It might make scholars less willing to perform reviews.
You may argue that this process should change, but this is the rationale.