Who was the naked prophet?

While all the prophets may match this description at least once in their lives (Eccl. 5:15), the specific incident you are no doubt referring to is that of the prophet Isaiah in Isaiah 20:1-6.

In the year that the supreme commander, sent by Sargon king of Assyria, came to Ashdod and attacked and captured it at that time the LORD spoke through Isaiah son of Amoz. He said to him, "Take off the sackcloth from your body and the sandals from your feet." And he did so, going around stripped and barefoot. Then the LORD said, "Just as my servant Isaiah has gone stripped and barefoot for three years, as a sign and portent against Egypt and Cush, so the king of Assyria will lead away stripped and barefoot the Egyptian captives and Cushite exiles, young and old, with buttocks bared to Egypt's shame. Those who trusted in Cush and boasted in Egypt will be afraid and put to shame. In that day the people who live on this coast will say, 'See what has happened to those we relied on, those we fled to for help and deliverance from the king of Assyria! How then can we escape?' "

One might say that Isaiah was the naked prophet; however, one should note that it is not believed he was totally naked. According to Carl Friedrich Keil and Franz Delitzsch:

With the great importance attached to the clothing in the East, where the feelings upon this point are peculiarly sensitive and modest, a person was looked upon as stripped and naked if he had only taken off his upper garment. What Isaiah was directed to do, therefore, was simply opposed to common custom, and not to moral decency. He was to lay aside the dress of a mourner and preacher of repentance, and to have nothing on but his tunic (cetoneth); and in this, as well as barefooted, he was to show himself in public. This was the costume of a man who had been robbed and disgraced, or else of a beggar or prisoner of war (Commentary on the Old Testament, 7:242, Peabody, MA: Hendrickson, 2002).