Mantriṇī-nyasta-rājyadhūḥ मन्त्रिणी-न्यस्त-राज्यधूः (786)

She has entrusted the ministerial responsibilities of the universe to MantriṇīMantriṇī is feminine gender for minister.  Her minister is Śyāmalā. There is already a reference to Mantriṇī in nāma-s 69 and 75. Śyāmalā is also known as Rāja-Mātaṅgī and Rāja-Śyāmalā.

It is also said that one who worships Her through mantra-s is known as mantriṇī. Here mantra-s do not mean Pañcadaśī and ṣodaśī alone. They are mantra-s of the highest order. Since She is mātṛkā varṇa rūpiṇī (nāma 577), all the alphabets belong to Her. All the letters originate from Her. Therefore, there is no distinction between Her and mantra-s.  This is confirmed by nāma 204. sarva mantra svarūpiṇīMantra is defined as ‘power in the form of formulated and expressed thought.’ This power is known as ŚaktīMantra-s are useful only if the deeper meaning of the mantra-s is understood. Mantra-s in combination with meditation give quicker results. Japa mantra-s do not fructify unless one understands the significance of mantra-s. Mantra-s are nothing but bījākṣara (combination of alphabets). A bīja is a monosyllabic sound that contains one or more consonants with a vowel and ends with a bindu. Vāmakeśvara Tantra (refer nāma-s 351 and 945) elaborates on mantra-s.

Śiva Sūtra (II.1) says Cittam mantraḥ (चित्तम् मन्त्रः). Cittam means limitation of the highest consciousness in the individual self. This can also be interpreted as the limitation of the Supreme Consciousness (the Brahman) in self (an individual). After having said that mind is mantra, the next sūtra (II.2) says that continuous effort leads to attainment (mantra siddhi or fructification mantra). The third sūtra (II.3) says the fructification mantra-s mean non-dualism or Oneness with the Brahman (Realisation). Mantra is nothing but a secret tool in the hands of a practitioner that first enables him to establish a link with the Brahman and ultimately making him to dissolve into the Brahman. When mind and mantra are well connected, one realises the Brahman.

This nāma also means that She is in the form such intricate and potent mantra-s. She is the sum total of all mantra-s.

Tripureśī त्रिपुरेशी (787)

Śiva had burnt Tripura, a place of asura-s (demons) fortified with gold, silver and iron forts. These are nothing but stages of ignorance. Śiva who burnt this place is known as Tripura and His wife is Tripureśī. This also means Bhairavī, the Goddess of Tantra śāstra-s. She is adored by all tantra śāstra-s. 

Or this could mean that She is the chief of three loka-s of Brahma, Viṣṇu and Śiva. These loka-s (worlds) are situated around Meru, where She resides (refer nāma 775. Meru-nilayā). (Tripura atipaṭhī (atipaṭhī means chief). 

Jayatsenā जयत्सेना (788)

She has a victorious army.  She is capable of winning over demons (evil acts). In Hindu scriptures, often references are made to demons. These demons are embodiment of wickedness and gods who win over them represent virtues.  Virtues always prevail.

Nistraiguṇyā निस्त्रैगुण्या (789)

She is devoid of three guṇa-s. These guṇa-s in association with prakṛti are responsible for creation. Please refer nāma-s 139, 397, 398 and 399 for further details.