Jankinath Kaul Kamal explains the meaning of This Name of Shreemati Parvati-Devi in his glosses to "Shreemati Bhavani-Sahasranam" from "Shree Rudra-Yamala-Tantra":
१७७. भगवती
177. BhagavatI
"The Supreme Divinity.
In accordance with
the lexical meaning, the Puranas say that "the full supremacy, righteousness, fame, prosperity, wisdom, discrimination": these six are called Bhaga ("Shree Vishnu-Purana", 6.5.74):
the lexical meaning, the Puranas say that "the full supremacy, righteousness, fame, prosperity, wisdom, discrimination": these six are called Bhaga ("Shree Vishnu-Purana", 6.5.74):
ऐष्वर्यस्य समग्रस्य धर्मस्य यशसः श्रियः ।
ज्ञानवैराग्ययोश्चैव षण्णां भग इतीरणा । ।
aiShvaryasya samagrasya dharmasya yashasaH shriyaH |
j~nAnavairAgyayoshchaiva ShaNNAM bhaga itIraNA | |
Because of these attributes the Divine Mother is called Bhagavati.
Shiva assumes Splendour only in Her company and undertakes the wonderful sport of manifestation and deliberation of this universe:
शोभां विभक्ति गिरिजे तव माहचर्यात्
shobhAM vibhakti girije tava mAhacharyAt
"Mother knows the origin and dissolution of the cosmos, the going and coming of beings, knowledge and ignorance, She is called Bhagavati" ("Shree Devi-Bhagavata-Purana"):
उत्पत्ति प्रलयं चैव भूतानामगतिगतिम् ।
अविद्याविद्ययोस्तत्वं वेत्तीति भगवत्यसौ । ।
utpatti pralayaM chaiva bhUtAnAmagatigatim |
avidyAvidyayostatvaM vettIti bhagavatyasau | |
"
Cited from
"BHAVANI NAMA SAHASRA STUTI
from RUDRAYAMALA TANTRA",
translated and annotated by
Jankinath Kaul Kamal,
RamaKrishna Ashram,
Shrinagar-Kashmir,
1991 - LINK TO E-BOOK
