Jayadeva Gosvāmī’s ten prayers worshiping the incarnations of Lord Kṛṣṇa (Keśava) contain His name in every stanza. For example, keśava dhṛta-nara-hari-rūpa jaya jagad-īśa hare, keśava dhṛta-mīna-śarīra jaya jagad-īśa hare, and keśava dhṛta-vāmana-rūpa jaya jagad-īśa hare. The word jagad-īśa refers to the proprietor of all the universes. His original form is the two-handed form of Lord Kṛṣṇa, standing with a flute in His hands and engaged in tending the cows. As stated in Brahma-saṁhitā:
lakṣāvṛteṣu surabhīr abhipālayantam
govindam ādi-puruṣaṁ tam ahaṁ bhajāmi
“I worship Govinda, the primeval Lord, the first progenitor, who is tending the cows, yielding all desires, in abodes built with spiritual gems and surrounded by millions of purpose trees. He is always served with great reverence and affection by hundreds and thousands of goddesses of fortune.” From this verse we learn that Govinda, or Kṛṣṇa, is the ādi-puruṣa (the original person). The Lord has innumerable incarnations, exactly like the innumerable waves of a flowing river, but the original form is Kṛṣṇa, or Keśava.
Śukadeva Gosvāmī refers to Nṛsiṁhadeva because of Prahlāda Mahārāja. Prahlāda Mahārāja was put into great distress by his powerful father, the demon Hiraṇyakaśipu. Apparently helpless before him, Prahlāda Mahārāja called on the Lord, who immediately assumed the gigantic form of Nṛsiṁhadeva, half-lion and half-man, to kill the gigantic demon. Although Kṛṣṇa is the original person, one without a second, He assumes different forms just to satisfy His devotees or to execute a specific purpose. Therefore Jayadeva Gosvāmī always repeats the name of Keśava, the original Personality of Godhead, in his prayers describing the Lord’s different incarnations for different purposes.