The Corn Market and the Corn Exchange are the two terms traditionally used in Britain for these buildings - Googling them will show that there are entire squares and streets so named.
The question of what "corn" means is complex, but the simplest answer is that a corn is a single grain of a plant. Hence the compounds barleycorn, peppercorn, sweetcorn, cornflour... In Britain the commonest cereal was traditionally wheat, so corn (BE) = blé. In America it was Indian corn, i.e. maize, so corn (AE) = maïs.