My output is:

-----------------------------

Now run:

My output is:

in testB

For deleting first n number of chars, instead of writing 'n' dots(.), following pattern can be used -

^.\{n\}
so the sed can be changed to

cat testA |sed 's/^.\{n\}//' > testB

if you want to change all the file name as u required then this might help u

ls | while read file
do
file_req=`echo ${file} | sed 's/^.\{n\}//' `
mv ${file} ${file_req}
done