Per Army regulations, the socks my not have a logo. In reality (i.e. how it really works) they may not have a logo which is visible when worn with the athletic footwear. That is to say, it's generally ok in pracitce if the socks have "Hanes" embroidered on the toe, but no logo should be anywhere on the portion of the sock which protrudes from the shoe. Remember that during CBT they will have their drawers inspected, so it would be best to opt for a non-logo version.
If you sharpie what shows will they allow you to wear it?
With what, a white Sharpie?
In general, using a Sharpie on your clothes is frowned upon.
I should of clarified I was talking about the bands on compression shorts.
^ The problem is it is hard to find good quality compression shorts that don't have a logo on them- nike and underarmour both do.
Would a sponge-tipped bottle of shoe polish work to cover up the logos?
Does the military state why they don't want logos? Is it a they want everything to be uniform or a they don't want any misconceptions about a logo representing them?