Computation offloading (often to external computing resources over a network) has become a necessity for modern applications. At the same time, the proliferation of machine learning techniques has empowered malicious actors to use such techniques in order to breach the privacy of the execution process for offloaded computations. This can enable malicious actors to identify offloaded computations and infer their nature based on computation characteristics that they may have access to even if they do not have direct access to the computation code. In this paper, we first demonstrate that even non-sophisticated machine learning algorithms can accurately identify offloaded computations. We then explore the design space of anonymizing offloaded computations through the realization of a framework, called Camouflage. Camouflage features practical mechanisms to conceal characteristics related to the execution of computations, which can be used by malicious actors to identify computations and orchestrate further attacks based on identified computations. Our evaluation demonstrated that Camouflage can impede the ability of malicious actors to identify executed computations by up to 60%, while incurring modest overheads for the anonymization of computations.