In the name of his brother; shall be called and reputed his son. See Ruth 4:17. That his name be not put out of Israel; that a family be not lost. So this was a provision that the number of their families might not be diminished.
Related Commentaries of Deuteronomy 25:6
Deuteronomy 25:6
6 And it shall be, that the firstborn which she beareth shall succeed in the name of his brother which is dead, that his name be not put out of Israel.