What is Bhaj Nitaigour Radheshyam Japa Hare Krishna Hare Ram?

Is this a Mantra or a Harinaam?
If this Mantra is employed does it signify that we are chanting a form of namabhas?
Is it appropriate to refer to Nitai Gour and Radhe Shyam together?
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We see in the case of Sri Gouranga Mahaprabhu and the Six Goswamis of Vrindavan the words “nāmā-gāna”, which refer to chanting aloud and along with it is mentioned that “they keep the count of their recitations.” In this verse the Goswamis of Vrindavan as in the verses of Sri Gouranga Mahaprabhu are chanting aloud “while counting.” The word counting in both passages is saṃkhyā, “sankhya-purvaka-nama-gana”. Samkhya translates in Sanskrit as “to number.” Further, there are no verses that indicate that some of them chanted the Maha Mantra in Kirtan. Instead, they do Harinam Kirtan as instructed by Sri Gouranga, as we cite here in Sri Chaitanya Bhagavata and Srila Rupa Goswami:
They should sing:
haraye namaḥ kṛṣṇa yādavāya namaḥ
gopāla govinda rāma śrī madhusūdana.
— CB 2.23.80
liebre krsnety-uccaih sphurita-rasano “nama-ganana”
Krta-granthi-sreni-subhaga-kati-sutrojjvala-karah visalakso
dirghargala-yugala-khelascita-bhujah sa chaitanyah
kim me punar api drsor yasyati padam
Sri Chaitanya Mahaprabhu chants the Hare Krishna Maha Mantra aloud, the Holy Name dances on his tongue, while he counts the number of recitations on a beautiful, knotted cord in his refulgent right hand. His eyes are large and his arms long, they bend as he carries out his pastimes, reaching his knees. Will he ever again cross the path of my eyes?
— Srila Rupa Goswami – Prathama Chaitanyastaka, 5
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