As set out in the policy (see details), consumer peer reviewers are exempt from the named peer review process and may choose to remain anonymous. (Consumers still follow the policy for Declarations of potential conflicts of interest for peer reviewers.)
Exceptions approved by Network Senior Editor or Editor in Chief
If a Cochrane Review Group believes that the peer review process for a particular Cochrane Review will be significantly negatively impacted by using named peer review, the Managing Editor or Co-ordinating Editor may apply to the Network Senior Editor or Editor in Chief of the Cochrane Library for a policy exception on a review-by-review basis. In each case the Cochrane Review Group must provide details, including the reason for opting to remain anonymous. Any exemptions must be forwarded to the Cochrane Editorial & Methods Department (firstname.lastname@example.org); see Exceptions to named peer review: editorial management.