Yes, that's generally how people and children were identified, by their paternity, particularly males it seems. Read the genealogies or any other number of passages:You read it....his son....not hers....
Gen 25:19 These are the generations of Isaac, Abraham's son: Abraham fathered Isaac, (ESV)
Mat 1:1 The book of the genealogy of Jesus Christ, the son of David, the son of Abraham.
Mat 1:2 Abraham was the father of Isaac, and Isaac the father of Jacob, and Jacob the father of Judah and his brothers,
Mat 1:3 and Judah the father of Perez and Zerah by Tamar, and Perez the father of Hezron, and Hezron the father of Ram,
Mat 1:4 and Ram the father of Amminadab, and Amminadab the father of Nahshon, and Nahshon the father of Salmon,
Mat 1:5 and Salmon the father of Boaz by Rahab, and Boaz the father of Obed by Ruth, and Obed the father of Jesse,
...
Mat 1:15 and Eliud the father of Eleazar, and Eleazar the father of Matthan, and Matthan the father of Jacob,
Mat 1:16 and Jacob the father of Joseph the husband of Mary, of whom Jesus was born, who is called Christ. (ESV)
Mat 16:17 And Jesus answered him, “Blessed are you, Simon Bar-Jonah! For flesh and blood has not revealed this to you, but my Father who is in heaven. (ESV)
Luk 5:10 and so also were James and John, sons of Zebedee, who were partners with Simon. And Jesus said to Simon, “Do not be afraid; from now on you will be catching men.” (ESV)
If you believe Isaiah had another wife then, please, provide the scriptural support.
Isa 7:3 And the LORD said to Isaiah, “Go out to meet Ahaz, you and Shear-jashub your son, at the end of the conduit of the upper pool on the highway to the Washer's Field. (ESV)
Isa 8:3 And I went to the prophetess, and she conceived and bore a son. Then the LORD said to me, “Call his name Maher-shalal-hash-baz;
...
Isa 8:18 Behold, I and the children whom the LORD has given me are signs and portents in Israel from the LORD of hosts, who dwells on Mount Zion. (ESV)
Isaiah had a wife and two sons. The prophecy in Isa 7:14 cannot be referring to his wife.