Monohydroxy alcohol has a Debye relaxation process that other liquids usually do not have, and with the further research, some new phenomena and new problems related to the process have been gradually discovered, deepening the understanding of material structure and dynamics. In order to further investigate the dynamics of Debye relaxation processes and the influence of molecular constitutions on them, the Debye processes of three primary alcohols without branched chains or side groups are studied by dielectric spectroscopy method, and some important information about the processes is revealed. A number of dynamic parameters of Debye relaxation in n-propanol, n-butanol and n-octanol almost all increase linearly with the rising of the number of carbon atoms in the molecules, which include the characteristic temperature, the reciprocal of Vogel-Fulcher-Tammann (VFT) temperature, the strength parameter of Debye process, the activation energy and the logarithm of the intrinsic vibration frequency of relaxation units under high temperature limit. However, the values of VFT temperatures change little and have consistency, illustrating that the relaxation units of Debye processes in these three monohydroxy alcohols should be the same, further verifying the view that the Debye relaxation originates from the hydroxyl groups in hydrogen bonded molecular chains. Comparing Boiling temperatures and melting temperatures of those samples with the evolution of the above activation energy, it is shown that there is a positive correlation between the interaction among hydrogen bonds and the whole one among molecules. In addition, combining the information about the strength parameter with that from the relevant theories, a possible perspective is gained for further investigation of liquid fragility. The comparison of those three samples with ethanol displays that the degree of separation of Debye relaxation and α relaxation is influenced by the molecular chain length, which can provide a breakthrough point to explore Debye relaxation. These results in this work will promote the further understanding and research of Debye relaxation in monohydroxy alcohols, and also provide experimental information for relevant theories.