If you have no imperfections in the structure, you can then build this structure (whatever it is) with a minimal unit cell and calculate the dynamical matrix for this cell, using some repetitions along the three lattice vectors of your minimal unit cell.
More repetitions you set for this calculation - more accurately the phonon band structure will be computed. Even so, you adopt repetitions, i.e., de-facto doing supercell calculations, the phonon bands will be computed and visualized for the minimal unit cell, i.e., the bands are given in the Brillouin zone of the minimal unit cell adopted, not the supercell.
If the minimal unit cell of the graphene-Cu system is not a primitive cell of a graphene sheet, then you have a natural folding of the phonon bands of the Cu-graphene hybrid system and that cannot be avoided. It might be that you could do an (approximate) unfolding using the spectral function to get an effective band structure, as done for electronic bands in Phys. Rev. B 85, 085201 – Published 2 February 2012, but I am not aware of any code doing it for phonon band structures.