Caitanya Mahaprabhu took sannyasa from Kesava Bharati. This Kesava Bharati belonged to Sankara sampradaya. Therefore Prakasananda Sarasvati also belonged to Sankara sampradaya. So he's asking that, - I understand that Your name is Sri Krsna Caitanya

Expressions researched:
"Caitanya Mahāprabhu took sannyāsa from Keśava Bhāratī. This Keśava Bhāratī belonged to Śaṅkara-sampradāya. Therefore Prakāśānanda Sarasvatī also belonged to Śaṅkara-sampradāya. So he's asking that, "I understand that Your name is Śrī Kṛṣṇa Caitanya"

Lectures

Sri Caitanya-caritamrta Lectures

It is not that you take your cloth and get it colored and one day you become a sannyāsī. No. There are ceremonies. So Caitanya Mahāprabhu took sannyāsa from Keśava Bhāratī. This Keśava Bhāratī belonged to Śaṅkara-sampradāya. Therefore Prakāśānanda Sarasvatī also belonged to Śaṅkara-sampradāya. So he's asking that, "I understand that Your name is Śrī Kṛṣṇa Caitanya.".

670208 - Lecture CC Adi 07.69-75 - San Francisco

The rule is that if one has to accept renounced order of life, there is ceremony. As there is ceremony of initiation, there is ceremony of accepting this renounced order of life. And that ceremony must be performed by another bona fide, I mean to . . . sannyāsī, renounced order. It is not that you take your cloth and get it colored and one day you become a sannyāsī. No. There are ceremonies.

So Caitanya Mahāprabhu took sannyāsa from Keśava Bhāratī. This Keśava Bhāratī belonged to Śaṅkara-sampradāya. Therefore Prakāśānanda Sarasvatī also belonged to Śaṅkara-sampradāya. So he's asking that, "I understand that Your name is Śrī Kṛṣṇa Caitanya."

Now, there are different kinds of names of brahmacārī also under the guidance of a sannyāsī. So the person who is under the guidance of Bhāratī, the brahmacārī's name is Caitanya. So Caitanya Mahāprabhu, although He took sannyāsa, He did not change His brahmacārī name. That is also very significant.