“Gauḍīya” indicates the part of India between the southern side of the Himalayan Mountains and the northern part of the Vindhyā Hills, which is called Āryāvarta, or the Land of the Āryans. This portion of India is divided into five parts or provinces (Pañca-gauḍadeśa): Sārasvata (Kashmir and Punjab),Kānyakubja (Uttar Pradesh, including the modern city of Lucknow), Madhya-gauḍa (Madhya Pradesh), Maithila (Bihar and part of Bengal) and Utkala (part of Bengal and the whole of Orissa). Bengal is sometimes called Gauḍadeśa, partly because it forms a portion of Maithila and partly because the capital of the Hindu king Rāja Lakṣmaṇa Sena was known as Gauḍa. This old capital later came to be known as Gauḍapura and gradually Māyāpur.
The devotees of Orissa are called Uḍiyās, the devotees of Bengal are called Gauḍīyas, and the devotees of southern India are known as Drāviḍa devotees. As there are five provinces in Āryāvarta, so Dākṣiṇātya, southern India, is also divided into five provinces, which are called Pañca-draviḍa. The four Vaiṣṇava ācāryas who are the great authorities of the four Vaiṣṇava disciplic successions, as well as Śrīpāda Śaṅkarācārya of the Māyāvāda school, appeared in the Pañca-draviḍa provinces. Among the four Vaiṣṇava ācāryas, who are all accepted by the Gauḍīya Vaiṣṇavas, Śrī Rāmānuja Ācārya appeared in the southern part of Andhra Pradesh at Mahābhūtapurī, Śrī Madhva Ācārya appeared at Pājakam (near Vimānagiri) in the district of Mangalore, Śrī Viṣṇusvāmī appeared at Pāṇḍya, and Śrī Nimbārka appeared at Muṅgera-patana in the extreme south.
Śrī Caitanya Mahāprabhu accepted the chain of disciplic succession from Madhva Ācārya, but the Vaiṣṇavas in His line do not accept the tattva-vādīs, who also claim to belong to the Mādhva-sampradāya. To distinguish themselves clearly from the tattva-vādī branch of Madhva’s descendants, the Vaiṣṇavas of Bengal prefer to call themselves Gauḍīya Vaiṣṇavas. Śrī Madhva Ācārya is also known as Śrī Gauḍa-pūrṇānanda, and therefore the name Mādhva-Gauḍīya-sampradāya is quite suitable for the disciplic succession of the Gauḍīya Vaiṣṇavas. Our spiritual master, Oṁ Viṣṇupāda Śrīmad Bhaktisiddhānta Sarasvatī Gosvāmī Mahārāja, accepted initiation in the Mādhva-Gauḍīya-sampradāya.
Ref >> Srila Prabhupada Vani.