In this week's Parsha, the Torah says, הקבצו ושמעו בני יעקב ושמעו אל ישראל אביכם, "Assemble and hear, O sons of Yaakov and hearken to Yisrael, your father" (בראשית מט:ב). Why is Yaakov referred to with two different names in the Pasuk? Knowing what each name means will help to understand why they are both used.
The Patriarch's name which had been given to him at birth was Yaakov. Accordingly, Jews are regarded "as children of Yaakov" by virtue of their descent from Yaakov and of their being part of the Jewish nation. However, the name "Yisrael" was not given to Yaakov until much later in life, when he attained the high moral level that made him worthy of it. "For thou hast striven with God and with men and hast prevailed." For this reason, the name "Yisrael" is used when applied to the Jewish people as a whole and signifies the high moral level of Bnai Yisrael as the spiritual heirs of Yaakov (also see Rabbi Joseph B. Soloveitchik's classic essay "קול דודי דופק" where he makes these distinctions based on a difference between מחנה and עדה as well as יעוד מצרים and יעוד סיני the "Jewish Destiny" as defined by the Exodus from Egypt as opposed to the "Jewish Destiny" as defined by the Sinai experience).
This can explain why the Torah uses both names in one Pasuk. When the Pasuk says, "Assemble and hear, O sons of Yaakov," this is used to call all of his sons for his last words. Yaakov begins by imparting the message to his children that you are united as the children of Yaakov, all sharing one descent and nationality. However, mere national ties are not enough. Yaakov emphasizes that you must also "hearken to Yisrael, your father." We see that before can reach to a higher spiritual level, we must first be able to band together on a national level.