Technically, to be unambiguous, you should say immediately after the sixth person on the list. His name could be at present in the 35th position on the list which satisfies the condition of being after the 6th person. You may accuse me of nit-picking.
As always, you could say the same thing in fewer words, tufguy.
'Let me move his name to seventh in the list.'
(I prefer 'move', but 'shift' is grammatical.)
Let me shift his name down or up the list. His name should be immediately after the sixth person on the list.
You don't need quotation marks here.
I am not a teacher.
Let me shift his name down or up the list. His name should be immediately before the sixth person on the list. Is it correct as well?
You literally just took my quote, dude.
Yes, but I would like to know about "before". Is it also correct to use "before" in place of "after" here?