The story goes that the Goddess Parvati was so determined to make Shiva her consort after all reasonable attempts to win him failed, that she went into the forest and performed rigorous tapas, wearing nothing to protect her body from harsh weather, eating nothing, not even a leaf, earning the admiration of forest ascetics who named her Aparna ("without leaves"). Aparna matched Shiva in her capacity to cut herself from the world and completely master her physical needs. The power of her tapas shook Shiva out of his meditation. She stepped out of his cave and accepted Parvati as his wife.
Another patriarchal story, but is it really that surprising? I am convinced there was a time several millenia back when Shiva did tapas to win Parvati. She is after all the Mother Goddess. Maybe she was named Aparna because he had to match her tapas and go without wearing or eating leaves before she would relent and relieve his love-sickness.
I have been told that Aparna is a classical Indian name, but so is Mary.