The CMB is sometimes referred to as an image of the last-scattering-surface. The photons reaching us now were last scattered at the time the Universe cooled enough for electrons to bind to protons and became largely transparent. However, this is only a "surface" in the sense that the photons reaching us now all have the same travel time and come from the same distance. At different times, the photons arrive from different distances. Since the entire Universe became transparent at roughly the same time, it's perhaps helpful to think about a last scattering "volume", which fills the entire Universe. At the time of last-scattering, the surface would be immediately surrounding the Earth (well, the matter that would eventually form the Earth, since it didn't exist yet), and move outwards with time to reach its present distance. The "last-scattering-volume" has, of course, hotter (underdense) and cooler (overdense) regions, scattered in 3D space, so as the last-scattering-surface intersects different slices through the volume, the pattern changes smoothly. The statistics of the pattern should remain the same, though, at least assuming what we think we know about cosmology.
There are other late time effects as well. For instance, the CMB is gravitationally lensed by large scale structure, notably galaxy clusters. As CMB photons arriving later will have crossed more evolved structure, they will be more strongly lensed, which will introduce a stronger overall distortion in the pattern. Or there's the Sunyaev-Zel'dovich effect, which is the net boost that CMB photons crossing regions of high relativistic electron density (i.e. galaxy clusters) get. Photons arriving later cross more & bigger clusters (at least until dark energy suppresses structure formation), so the SZ effect is enhanced.