  The pseudorapidity density of charged particles,
$\rm{d}\it{N}_\rm{ch}/\rm{d}\it{\eta}$, in p-Pb collisions has been measured at
a centre-of-mass energy per nucleon-nucleon pair of $\sqrt{s_{\rm{NN}}}$ = 8.16
TeV at mid-pseudorapidity for non-single-diffractive events. The results cover
3.6 units of pseudorapidity, $|\eta|<1.8$. The
$\rm{d}\it{N}_\rm{ch}/\rm{d}\it{\eta}$ value is $19.1\pm0.7$ at $|\eta|<0.5$.
This quantity divided by $\langle N_\rm{part} \rangle/2$, is $4.73\pm0.20$,
which is 9.5% higher than the corresponding value for p-Pb collisions at
$\sqrt{s_{\rm{NN}}}$ = 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
$\rm{d}\it{N}_\rm{ch}/\rm{d}\it{\eta}$ distribution. Saturation-based models
reproduce the distributions well for $\eta>-1.3$. The
$\rm{d}\it{N}_\rm{ch}/\rm{d}\it{\eta}$ 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.
