You need to do that through the Visitor Center staff when you pick up the permit the day before your hike. Adding a person is permitted only if a slot is available.
We are told that during the time when other groups are picking up their reserved permits (two days before the hike, up until the pickup deadline, 1 pm the day before the hike), the other groups often drop a slot or two, and those slots immediately become available to others.
So if you are lucky, you can add one of those. If not, then at 2 pm the day before the hike, the no-shows are made available. There are usually quite a few of those, and a drawing of numbers to determine who gets first shot at those is held at the 2 pm time.
If you check several times between ~9 and 1, you are likely to get the extra slot. And if not, then also likely at 2 pm.
Edit: Not sure if this would work, but if you asked people going in if they were picking up day hike permits and also dropping one, if you got in line right behind them, the dropped slot could be yours. Nothing wrong with your extra being added to the other group by that group's leader, too, if leader is willing.
Edited by Steve C (08/17/12 12:52 AM)