  We report field-dependent high-resolution inelastic neutron scattering (INS)
measurements on the honeycomb lattice magnet, CoTiO$_3$, to study the evolution
of its magnon excitations across a spin reorientation transition driven by an
in-plane magnetic field. By carrying out elastic neutron scattering in a
magnetic field, we show that the sample transitions from a collinear
antiferromagnetic state with multiple magnetic domains at a low field to a
mono-domain state with a canted magnetic structure at a high field. Concurrent
with this transition, we observed significant changes in both the energy and
the width of the zone center magnon peak. The observed width change is argued
to be consistent with an unusual zero-field state with extended domain walls.
On the other hand, the magnon spectra near the $\mathbf{K}$ point of the
Brillouin zone boundary are found to be largely insensitive to the changes in
the ordered moment directions and the domain configuration. We argue that this
observation is difficult to explain within the framework of the bond-dependent
model proposed in a recent INS study [Elliot \textit{et\,al}, Nat. Commun.,
\textbf{12}, 3936 (2021)]. Our study therefore calls for alternative
explanations for the observed $\mathbf{K}$-point gap in CoTiO$_3$.
