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From this blog which answers Who are Gaudiya Vaishnavas?

“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.

So the word “Gauḍīya” in Gauḍīya Vaiṣhṇavism refers to a geographic area known as Gauḍadeśa.