I think "minimum viable product" works, and is better than "minimum desirable product" at describing the goal, since to be viable as a product something must not only be desired, but be desired by customers willing to pay for it sufficiently to meet the marginal costs of delivering it.
Of course, an MVP can fail to be viable as a product and still deliver validated learning (as I understand, the original definition of the purpose an MVP) that progresses you toward something viable as a product, but the goal at each iteration should be to have something valuable as a product (and this is consistent with the more general lean methods which lean startup draws on, where each iteration aims to do the minimum work that will produce independent business value.)