The One whose tapsya was without even the basic leaf for sustenance.
This name reflects Maa Parvati’s Tapasya and in this ascetic form where Her devotion and sadhana makes Her give up all attachments to identity and to the material world. Where She chooses severe penance to win over Lord Shiva. Kaalika as Maa, Parvati attains the name Aparna, when she gives up even leafs for sustenance in the tapsya for MahaDeva.
The name denotes she was Maa Parvati.
Hence the name, Aparna.