शौर्यातिशयेनेष्टे इति शूरजनेश्वरः ।त्रयाणां लोकानाम् अ न्तर्यामितया आत्मेति, त्रयो लोका अस्मात्परमार्थतो न भिद्यन्ते इति वा त्रिलोकात्मा ।त्रयो लोकाः तदाज्ञप्ता: स्वेषु स्वेषु कर्मसु वर्तन्त इति त्रिलोकेशः ।केशसंज्ञिता: सूर्या दिसंक्रान्ता अंशवः, तद्वत्तया केशवः; 'अंशवो ये प्रकाशन्ते मम ते केशसंज्ञिताः ।सर्वज्ञाः केशवं तस्मान्मामाहुर्द्विजसत्तमाः' इति महाभारते ।ब्रह्मविष्णुशिवाख्याः शक्तयः केशसंज्ञिता:; तद्वत्तया वा केशवः ।त्रयः केशिनः इति श्रुतेः ।'मत्केशौ वसुधातले' इति केशशब्दः शक्तिपर्यायत्वेन प्रयुक्तः ।'को ब्रह्मेति समाख्यात ईशोऽहं सर्वदेहिनाम् ।आवां तवांशसंभूतौ तस्मात्केशवनामवान्' इति हरिवंशे ।केशिनामानमसुरं हतवानिति केशिहा ।सहेतुकं संसारं हरतीति हरिः ।
In plain words
He is called Śūrajaneshvara because He is yearned for through His supreme valor. He is Trilokātmā because the three worlds are not separate from Him, who dwells within them as their inner Self. He is Trilokeśa because all worlds fulfill their duties under His command. He is Keśava because His are the rays of light called keśas—as the Mahābhārata records: 'The shining rays are My keśas; therefore, best of twice-born, the omniscient call Me Keśava.' Or He is Keśava because the cosmic potencies of Brahmā, Viṣṇu, and Śiva are His rays, the Vedas speaking of three such entities, and the word keśing being used for power. As the Harīvaṃśa declares: 'Who is Brahman? I am the lord of all bodies; we both are born of your parts, hence You are Keśava.' He is Keśihā because He destroyed the demon Keśin. And He is Hari because He removes saṃsāra along with its root cause.
Close to the Sanskrit
Desired due to excess of bravery, thus Shurajaneshvara. Trilokatma, because the three worlds do not differ fundamentally from Him as the inner controller. Trilokesha, because the three worlds exist in their respective duties commanded by Him. Keshava, due to possessing the solar rays and other light forms termed keshas; as stated in the Mahabharata, 'Those rays which shine are my rays termed keshas, therefore omniscient ones call me Keshava, O best of the twice-born.' Or Keshava, due to possessing the potencies named Brahma, Vishnu, and Shiva, since the Shruti says 'three Keshis.' The word kesha is used as a synonym for shakti, as in 'my two hairs on the earth.' 'Who is Brahman declared to be? I am the lord of all embodied beings; we two are born from your part, therefore bearing the name Keshava,' as in the Harivamsha. Keshiha, because He slew the demon named Keshi. Hari, because He removes samsara along with its cause.