Ah, but it only takes a little history to make the connection clear! Mother Adélie Hubbard was the mother superior of a small convent of Spheniscidan nuns in pre-Reformation London. Toward the end of her life, the nuns were called to feed a nearby community of Dominican friars decimated by a famine. The nuns themselves were on the verge of starvation but nonetheless were inspired by Mother Hubbard to heed the call.
The first verse of the popular children's nursery rhyme is a reference to this event: Old Mother Hubbard is of course the mother superior herself; the cupboard represents the convent's food stores; the Dominicans were known as the "dogs of God" (a Latin pun: Domini canes); a bone makes a poor meal, symbolizing the fact that the nuns had little to spare; and of course, the cupboard was bare -- starvation ultimately wiped out both communities. (Subsequent verses are later additions, and probably just pleasant nonsense.)
The dress, as you can see, got its name from its loose fit -- as on an emaciated nun -- and its lack of a belt. Spheniscidines wear no adornment of any kind, including belts.
More on this etymology from cultural linguist and medieval English scholar Gentoo Humboldt at the Royal Fiordland University in Oslo.