In Open Computing Environments, more and more applications are deployed as service. They provide services for users from different organizations. Resources are deployed different organizations or enterprises. Users could access them across organizational boundaries. To ensure the security of resources, users have to provide their identity information to be authorized correctly every time they access a new service. It raises the risk of privacy which identity information was transferred frequently. In this paper, we demonstrate the problem of privacy in Identity Management of open computing environments, discuss the risk of privacy.