I would suggest using furniture 'Burn-In Sticks' available from a
company such as Behlen.  These are varnish sticks in various shades
designed to be applied with a hot knife to the depressed or gouged area
and smoothed in.  The surface is then 'grained' with a graining pen of
a suitable (darker) color and the whole sealed with a clear sealer.

Much art is involved, and I would suggest hiring a skilled furniture
repairer.  I had this done to a piece of furniture and you cannot see
where it was done, but it does require skill, especially in blending
the grain.  I'm in the process of learning the art, but I expect to
make several 'messes' along the way (on practice pieces).  I doubt very
much whether the wood can be satisfactorily raised back up to level
once it has been 'compressed' by a furniture mover!

Hal Estry