From his loss of Yosef until this juncture, the Torah refers to the Patriarch as Yaakov. This is the first instance in which the Torah refers to him with the name Yisrael, signifying strength. The name Yaakov implies a depressed state of mind in which one feels despondent It describes one who is “limping behind” circumstances (as in uag ceg – Eisav’s heel), unable to master over them.
Horav S.R. Hirsch, z.l., explains his sudden change in the following manner: The believing Jew only feels despondent when he is at a loss to know what he should do. The righteous Jew becomes depressed by two things: guilt for having done wrong and doubt regarding the correct course of action to follow. He never fears the future, for he places his complete trust in Hashem. As long as Yaakov was in doubt about whether or not he should allow Binyamin to leave, his name appears as Yaakov.
From the moment that his departure seemed a pressing necessity because his life was in peril (whether he stayed home and starved or he went on the treacherous trip), Yaakov culled his resources and became Yisrael. As soon as a Jew realizes it is beyond his human powers to provide for himself, he is told, ‘s kg kud (Tehillim 37:5) “roll over to Hashem.” This refers to that which is too difficult for one to handle alone. Therefore, with quiet resolve, the Patriarch reproached his sons only for having unnecessarily mentioned their youngest brother at all. In regard to the future, however, he placed his resolute faith in Hashem.