Is there additional significance to the name Efrayim (above what Yosef said)?
Da'as Zekenim, Hadar Zekenim: He was named so based on two of the Avos 1 - Avraham said "v'Anochi Afar va'Efer" (18:27), and Yitzchak became ashes on the Mizbe'ach [at the Akedah].
Malbim: Hashem made me fruitful specifically in the land of my affliction; affliction causes greatness.
Oznayim la'Torah: As time moved on, Yosef began to long for the spiritual environment of his father's house, as opposed to the Tum'ah of his current surroundings, so, with the birth of his second son, he referred to Egypt as 'the land of my suffering.'
Da'as Zekenim: Efrayim is like the plural of Efer. All of Yisrael are called Efrayim - "ha'Ven Yakir Li Efrayim" (Yirmeyahu 31:19). (It does not seem that he means only Malchus Yisrael, to exclude Malchus Yehudah. Radak (to Yirmeyahu 31:8) holds that Efrayim refers only to the 10 Shevatim - PF.)