There's no mystery about how the alligator pepper got its name. Within the gnarly pod are dozens of seeds; a few are shown, poorly, in the lower right corner of the first photo. Though cardamom is a closer botanical relative, the dried seeds resemble small peppercorns and, in West Africa, have similar culinary uses. Medicinal uses, too: A fellow customer offered that a few seeds, swallowed with honey, help to clear the lower respiratory tract.
Can the seeds also properly be called "grains of paradise," which some marketers maintain is a distinct and superior spice? Especially in Nigeria, the previous home of this market's proprietor, both alligator pepper and grains of paradise have been identified with Aframomum melegueta, even in the scientific literature. My own further research hasn't clarified the matter; it's not so much a mystery as a muddle.
Ola African Market
182-13 Jamaica Ave. (182nd St.-182nd Pl.), Hollis, Queens