When the leader gets their permit, they also get a tag for each hiker to wear in their own backpack. The tags are color-coded to differentiate between overnight and day use, and have the permit number on them (I think). To yes, it's just fine to hike separately, as far as permits go.
On the other hand, many search and rescue operations involve a hiker left behind by others. It is really bad form to separate, when the one(s) left behind are less experienced, and can get into trouble -- off trail, in the dark, etc. Do not leave slower ones to descend on their own! Bearing that in mind, have a safety plan in place; make sure everyone in the group knows where they are, where they are going, and what they should do in case you don't meet up again at the agreed/planned on time and place.
