Tripurā त्रिपुरा (626)
There is an ancient scripture titled Tripura rahasya in the form of dialogue between sage Bhārgava and sage Dattatreya. The original text consists of three parts – The glory of Devi, Her rituals and knowledge about Her.
This nāma could also mean that She is in the form of all triads. For example, She is in the form of Brahma, Viṣṇu and Rudra; Icchā, jñāna and kriyā śakti-s; the three kūṭa-s of Pañcadaśī; creation, sustenance and destruction; the three nādi-s, iḍā, piṅgala and suṣumna; three worlds, bhūr, bhuva, suvaḥ; three guṇa-s sattvic, rajasic and tamsic. She is in the form of all such triads and once these triads are transcended, the Brahman is attained.
Brahman is pure consciousness and can be visualized in three ways. The first one is paramātṛ-caitanya (consciousness limited by intellect). The second one is pramāṇa-caitanya (consciousness limited by knowledge). The third one is jīva-caitanya (consciousness limited by individual soul). These three types of consciousness are also known as triad.
Trijagad vandyā त्रिजगद् वन्द्या (627)
She is worshipped in all the three worlds viz. bhūr, bhuvar, suvar. The three worlds are represented by three vyāhṛti-s of Gāyatrī mantra. These three worlds are nothing but the three stages of consciousness. The lowest level of consciousness is materialistic in nature and the highest-level consciousness is pure in nature. The purest form of consciousness is the Brahman.
Trimurtiḥ त्रिमुर्तिः (628)
Trimurti-s are Brahma, Viṣṇu and Rudra. She is the combined form of these three Gods.
There is a story associated with this nāma. Brahma, Viṣṇu and Śiva looked at each other and in the process there appeared a young girl. On seeing the girl, these Lords asked her who she is. She replied saying that She is the Śaktī, the combined form of all the three of them. They named the girl as Tripura. Tripura form of Devi was born out of subtle looks of Gods of creation, sustenance and dissolution. She is made of three colours, white, black and red. White colour is Brahma. He is sattvic in nature and hence described as white. Next is black representing Viṣṇu’s rajo guṇa. The third colour is red, representing the red colour of Rudra, a form of Śiva, tamo guṇa. However, the guṇa-s of Brahma, Viṣṇu and Śiva are interpreted differently. It is said that the Brahman has divided into three, Brahma, Viṣṇu and Rudra. The same three combined to form Śaktī. She is One into many and many into One. That one is the Brahman. Brahman is the cause and Śaktī is the effect. For every cause there has to be effect/s.
This nāma says that She is in the form of the three guṇa-s and thus represents the three aspects of the Brahman - creation, sustenance and dissolution. Please refer nāma-s 763 and 984.
Tridaśeśvarī त्रिदशेश्वरी (629)
She is Īśvarī to all gods and goddesses. She is the Īśvarī of tri-daśa-s. In human, there are four stages – child, youth, middle age and old age. However, gods have only one stage of eternal youthfulness. Hence gods and goddesses are known as tri-daśa. She is the chief of all tri-daśa-s (gods and goddesses).
Tri means three and daśa means ten. 3 x 10 gives numeric 30. Another three is to be added to this making it as 33. Twelve Āditya-s, eight Vasu-s, eleven Rudra-s, and two Aśvin-s, thus making thirty three. She is the chief of all these thirty three gods. Each of these thirty three gods has 10,000,000 (ten million or one crore) assistants and they can be explained as demigods and demigoddesses. This explains 33 crore gods (330 million).
She is also the Īśvarī for three stages of human consciousness – sleep, dream and deep sleep stages.
Tryakṣarī त्र्यक्षरी (630)
She is in the form three bīja-s. For example, Bālā mantra has three bīja-s – aiṁ - klīṁ- sauḥ (ऐं- क्लीं- सौः). In ṣodaśī mantra, the three kūṭa-s of Pañcadaśī are treated as three bīja-s.
Bṛhadāraṇayaka Upaniṣad (V.iii.1) says that hṛdaya (हृदय) has three syllables (hṛ + da+ ya). In the same Upaniṣad it is also said (V.v.1) that satya (सत्य) has three syllables (sa + t + ya). Both heart and truth means the Brahman. All those that have three syllables lead to Her. For example, Brahman is said to be residing in the heart. satyaṁ jñānamanantaṁ is the Brahman.