[Advaita-l] Aparna Name of Parvati

[Venkata sriram P]

Namaste,
Apart from the explanation what you have mentioned, couple of other explanations were suggested by Shri Bhaskararaya and Shri Kalyananda Bharati Mantacharya.
1.  apagataM ruNaM yasyAssA taduktaM asmAbhiH dEvIstavE "ruNamiSTamadattvaivatvannAma japatO mama, shivE kathaM aparNEti rUDirbhArAya na tE".
Here, parNa implies riNa (debt). So, a-parNa implies in whom there are no debts. Since, dEvi doesn't have any debts with Her, she also removes those in Her upAsakAsby removing riNa-trayAs ie., 3 forms of debts (dEva, pitru & rishi).
2. parNa also means downfall or chyuti. So, a-parNa implies that state in whom there isno downfall (ref: achyutaH in viSNu saha.).
3. "a" kAra is brahmavAchaka and parNa implies vAhana. So, a-parNa implies brahmavAhana.  In order words, upAdhi of brahma.  
Hope it is clear now.
regs,sriram