Perhaps we can just call it a catch-all, and leave it at that. The two "cups" to the right suggest an insert I've seen in a Craftsman magazine plan for a "Mans Dressing Chest."
To quote the text (which doesn't match the illustration...), "The small upper drawer at the right, (sic) is fitted, like a change-drawer, with six saucer-like divisions for shirt, collar, and sleeve buttons, and other small objects which are easily lost."