Try to make something out of this
s1 = dir( fullfile( folder_1, '*.png' );
s2 = dir( fullfile( folder_2, '*.png' );
% name_list = union( {s1.name}, {s2.name} );
name_list = intersect( {s1.name}, {s2.name} ); % thanks to @Image
for jj = 1 : length( name_list )
name_list{jj}
end
 
Addendum
On Windows, upper and lower case might cause problems. ABC.png is the same name as abc.png. Replace
name_list = intersect( {s1.name}, {s2.name} );
by
name_list = intersect( lower({s1.name}), lower({s2.name}) );
