चतस्रो मूर्तयो विराट्सूत्राव्याकृततुरीयात्मानोऽस्यति चतुर्मुर्तिः; सिता रक्ता पीता कृष्णा चेति चतस्रो मूर्तचोऽस्येति बा ।चत्वारो बाह्वोऽस्येति चतुर्बाहुः इति नाम वासुदेवे रूढम् ।'शरीरपुरुषश्छन्दः पुरुषो वेदपुरुषो महापुरुष.' इति बह्वृचोपनिषदुक्ताश्चत्वारः पुरुषा व्यूहा अस्येति चतुर्व्यूहः ।आश्रमाणां वर्णानां चतुर्णा यथोक्तकारिणां गतिः चतुर्गतिः ।रागद्वेषादिरहितत्वात् चतुरः आत्मा मनोऽस्येति, मनोबुद्ध्यंकारचित्ताख्यान्तःकरणचतुष्टयात्मकत्वाद्वा चतुरात्मा ।धर्मार्थकाममोक्षाख्यपुरुषार्थचतुष्टयं भवत्युत्पद्यते अस्मादिति चतुर्भावः ।यथावद्वेत्ति चतुर्णां वेदानामर्थमिति चतुर्वेद॒वित् ।एकः पादोऽस्येति एकपात् ; ' पादोऽस्य विश्वा भूतानि' इति श्रुतेः 'विष्टभ्याहमिदं कृत्स्नमेकांशेन स्थितो जगन्' इति भगवद्वचनाच ॥समावर्तीऽनिवृत्तात्मा दुर्जयो दुरतिक्रमः ।दुर्लभो दुर्गमो दुर्गा
In plain words
He is Caturmūrti because his manifestations comprise the four states of Virāj, Sūtra, Avyākṛta, and Turīya, or because he assumes the four hues of white, red, yellow, and black. He is Caturbāhu because he possesses four arms, a name traditionally associated with Vāsudeva. He is Caturvyūha because the four cosmic puruṣas described in the Upaniṣad constitute his emanations. He is Caturgati as the ultimate refuge for all followers of the four traditional stages and orders of life. He is Caturātmā because his inner essence is completely free from passion and aversion, or because he encompasses the fourfold internal faculties of mind, intellect, ego, and memory. He is Caturbhāva because all four human aspirations originate from him. He is Caturvedavit because he perfectly comprehends the true import of the four Vedas. He is Ekapāt because the entire manifest universe is merely a single quarter of his infinite being, as confirmed by both the Vedic hymns and his own declaration in the Bhagavadgītā: 'Having supported this entire universe with a mere fraction of my being, I remain.' Then follow Samāvartī, Anivṛttātmā, Durjaya, Duratikrama, Durlabha, Durgama, and Durgā.
Close to the Sanskrit
Caturmūrtiḥ because whose four forms are Virāj, Sūtra, Avyākṛta, and Turīya; or because white, red, yellow, and black are four forms of his. Caturbāhuḥ because four arms belong to him, a name conventional in Vāsudeva. Caturvyūhaḥ because the four puruṣas stated in the Bāhṛca upaniṣad—body-puruṣa, meter-puruṣa, veda-puruṣa, and great-puruṣa—are his vyūhas. Caturgatiḥ because he is the goal of the four āśramas and four varṇas acting as prescribed. Caturātmā because his mind is unblemished being devoid of attachment and aversion, or because he consists of the fourfold internal organ consisting of mind, intellect, ego, and memory. Caturbhāvaḥ because the tetrad of human goals starting with dharma and artha arises from him. Caturvedavit because he accurately knows the meaning of the four Vedas. Ekapāt because a single foot belongs to him, based on the Śruti 'All beings are a quarter of him' and the Lord's statement 'Supporting this entire universe with a single fraction, I remain.' Samāvartī, Anivṛttātmā, Durjayaḥ, Duratikramaḥ, Durlabhaḥ, Durgamaḥ, Durgā.