It is so called because the building is done in twos, resulting in odd and even numbers.
When play goes to a stand still, the stock is dealt one a time.
To do this, the player can pick up the wastepile and turn it over to be used as the new stock.
Odd and Even is also closely related to Royal Cotillion, which has very similar game-play but has a reserve of sixteen cards.
This in turn is closely related to Contradance (Cotillion) and the single-deck game Captured Queens (Quadrille), both of which have no reserve and are entirely luck-based.