Rashi: They are of Yeshayah ¹ .

Rashi, from Bereishis Rabah 42:14: They are Talmidim, who are dear to me like children.

Radak: They are She'ar Yashuv (7:3) and "Maher Shalal Chash Baz" (8:3).

Malbim (3): The first was Achaz' son, and the second was Yeshayah's. They are not [both] my children; rather, He gave them to me for signs (refer to 8:3:2:2*).

Rashi: They are (a) a sign of punishments of Pekach - he called his son "Maher Shalal Chash Baz" (8:3), and (b) the salvation via natural means or people of Beis David, like he called his son Imanu'el (7:14).

Rashi, from Bereishis Rabah 42:14: The Talmidim are a sign that Torah will exist in Yisrael via them.

Radak: My actions for a sign, i.e. writing the scroll, and calling the names to my sons, was not my idea. It was from Hashem; He will save us from Melech Aram and Melech Ashur.

Malbim: The actions that I did - drawing on the parchment figures of people plundering (refer to 8:1:3:3) and signing Zecharyah and Uriyah on the Torah (refer to 8:16:2:4), Hashem commanded this. Surely He will not retract, since these actions were done to support the prophecies!