In this paper, we propose a new service orchestration approach for in-network fully distributed dynamic compute composition with limited involvement from the consumer and no centralized coordinator. The service is composed fully inside the network including assembling data and software, and compute node selection, leveraging standardized NDN functionalities. The use of the proposed approach will enable smooth support of dynamic compute services over wireless/mobile edge and edge/fog NDN-based systems, where the use of conventional IP approach faces fundamental difficulties related to dynamic allocation of IP addresses. We will also outline extensions of the proposed approach for streaming data, function chaining and re-use of partially computed results. Our numerical results show that the proposed method improves service reliability at the edge by increasing the Interest satisfaction by 5-10 times depending on the considered deployment, network topology, and resources.