What were the names of the two sons born to Joseph in Egypt?

Answer: Manasseh and Ephraim

Asenath bore Manasseh ("God has made me forget all my hardship") and Ephraim ("God has made me fruitful").

“Joseph named the firstborn Manasseh, saying, “God has made me forget all my hardship and all my father’s household.””— Genesis 41:51 (BSB)