We investigate the influence of Co intercalation and altermagnetic order on the lattice dynamics of the layered compound Co${}_{1/4}$NbSe${}_2$. Polarization-resolved Raman spectroscopy, supported by density-functional theory, enables identification of six Raman-active phonons. Co intercalation drives a substantial reconstruction of the vibrational spectrum through zone folding of NbSe${}_2$ phonons, producing hybridized modes with mixed zone-center and zone-boundary character. Despite this, Co atoms do not participate in any Raman-active modes by symmetry, which is in marked contrast to related $1/3$ compounds where intercalant modes do contribute to the Raman spectrum. Temperature-dependent Raman measurements across the altermagnetic transition show no discontinuities, which is consistent with magnetic fluctuations persisting above the N'eel temperature. However, we find evidence for spin-phonon coupling in $A_{1g}$ symmetry modes owing to their out-of-plane Se displacements. Our work demonstrates the substantial impact of intercalation on the vibrational properties of transition metal dichalcogenides and the presence of spin-phonon interactions in a newly discovered altermagnetic material.