The pseudorapidity density of charged particles, d N _ch / d η, in p–Pb collisions has been measured at a centre-of-mass energy per nucleon–nucleon pair of sNN = 8.16 TeV at mid-pseudorapidity for non-single-diffractive events. The results cover 3.6 units of pseudorapidity, | η| < 1.8. The d N _ch / d η value is 19.1 ± 0.7 at | η| < 0.5. This quantity divided by ⟨ N _part ⟩ / 2 is 4.73 ± 0.20 , where ⟨ N _part ⟩ is the average number of participating nucleons, is 9.5% higher than the corresponding value for p–Pb collisions at sNN = 5.02 TeV. Measurements are compared with models based on different mechanisms for particle production. All models agree within uncertainties with data in the Pb-going side, while HIJING overestimates, showing a symmetric behaviour, and EPOS underestimates the p-going side of the d N _ch / d η distribution. Saturation-based models reproduce the distributions well for η> - 1.3. The d N _ch / d η is also measured for different centrality estimators, based both on the charged-particle multiplicity and on the energy deposited in the Zero-Degree Calorimeters. A study of the implications of the large multiplicity fluctuations due to the small number of participants for systems like p–Pb in the centrality calculation for multiplicity-based estimators is discussed, demonstrating the advantages of determining the centrality with energy deposited near beam rapidity.