Fully homomorphic encryption (FHE) is a powerful cryptographic primitive to secure outsourced computations against an untrusted third-party provider. With the growing demand for AI and the usefulness of machine learning as a service (MLaaS), the need for secure training and inference of artificial neural networks is rising. However, the computational complexity of existing FHE schemes has been a strong deterrent to this. Prior works suffered from accuracy degradation, lack of scalability, and ciphertext expansion issues. In this paper, we take the first step towards the problem of space-efficiency in evaluating deep neural networks through designing DOReN: a low depth, batched neuron that can simultaneously evaluate multiple quantized ReLU-activated neurons on encrypted data without approximations. Our circuit design reduced the complexity of the accumulator circuit depth from <inline-formula> <tex-math notation="LaTeX">$O(\log m \cdot \log n)$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$O(\log m + \log n)$ </tex-math></inline-formula> for <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> bit integers. The experimental results show that the amortized processing time of our homomorphic neuron is approximately 1.26 seconds for 300 inputs and less than 0.13 seconds for 10 inputs at 80 bit security, which is a 20 fold improvement upon Lou and Jiang, NeurIPS 2019.