This is a Paint by Num-burr puzzle.
The letters in the initial grid can be ignored for now. Then, examination of the counts (especially cases like the 17th column) suggests that if it is to be a Paint-by-Numbers, blocks must be adjacent over the bars in the count lists, as is suggested by the formatting of the counts. The bars can then be drawn in the grid in the interiors of the shapes produced.
So doing produces something like
(where the colors are merely used to aid visualization for this solution; there's no reason to color them in the puzzle itself).
As highlighted by the colors above, there are 5 disjoint blobs in
the image, with heavier lines drawn across them. The heavy lines
are always drawn in such a way that the blob can be folded across
them, and in fact these are all nets of polycubes, which can be cut
out and folded up like so (colors are the same as the grid above):
Counting up the number of unit cubes shows there are 27,
suggesting the polycubes can be assembled into a 3x3x3 cube kind of
like a burr puzzle...
appropriately enough the lovely painting is becoming cubist. This
can be done in exactly one way, like this:
Finally, the letters from the original grid come into play.
Starting at the blue A in the upper corner of the left face shown
in the first image above, and reading around the cube is the string:
AVE RAG ETO PFA CEL ETT ERS WIT HBO TTO MFA CES
So, following the instructions, pairwise average the top face
WOQ FCS GATwith the bottom face
SUA HGE QIPto get
URI GEL LER
So the answer is URI GELLER.