We have studied the properties of photoluminescence (PL) from individual isoelectronic traps formed by nitrogen-nitrogen (NN) pairs in nitrogen atomic-layer doped (ALD) GaAs. Micro-PL measurements were performed to investigate the properties of single photons generated from individual isoelectronic traps. Twin PL peaks were observed from individual isoelectronic traps in nitrogen ALD GaAs(001). The PL transitions at longer and shorter wavelength sides were linearly polarized in the  and [1-10] directions, respectively. The peak splitting and polarization properties can be explained by some in-plane anisotropy most likely due to strain in host crystal. From individual isoelectronic traps in nitrogen ALD GaAs(111), a single PL peak with random polarization was observed, showing that the growth on (111) surface is an effective way to obtain unpolarized single photons. As for nitrogen ALD GaAs(110), different polarization properties were obtained depending on the atomic configuration of NN pairs. In addition, we have used AlGaAs layers to diminish the in-plane anisotropy and could successfully obtained single emission lines with unpolarized character. Introducing AlGaAs layers was also useful for improving the luminescence efficiency.