Śrīla Jīva Gosvāmī explains that kṛṣṇa-varṇam means Śrī Kṛṣṇa Caitanya. Kṛṣṇa-varṇa and Kṛṣṇa Caitanya are equivalent. The name Kṛṣṇa appears with both Lord Kṛṣṇa and Lord Caitanya Kṛṣṇa. Lord Śrī Caitanya Mahāprabhu is the Supreme Personality of Godhead, but He always engages in describing Kṛṣṇa and thus enjoys transcendental bliss by chanting and remembering His name and form. Lord Kṛṣṇa Himself appears as Lord Caitanya to preach the highest gospel.
Lord Caitanya always chants the holy name of Kṛṣṇa and describes it also, and because He is Kṛṣṇa Himself, whoever meets Him will automatically chant the holy name of Kṛṣṇa and later describe it to others. He injects one with transcendental Kṛṣṇa consciousness, which merges the chanter in transcendental bliss. In all respects, therefore, He appears before everyone as Kṛṣṇa, either by personality or by sound. Simply by seeing Lord Caitanya one at once remembers Lord Kṛṣṇa. One may therefore accept Him as viṣṇu-tattva. In other words, Lord Caitanya is Lord Kṛṣṇa Himself.

(Sri Caitanya Caritamrta-------1:3:52------purport).