Our forefather Jacob was later given an additional name -- Israel, which is why the Jews, his children, are referred to by both names.
The two names represent different virtues, both which are inherent within each Jew, and are exhibited at different points in one's life experiences.
In short, Jacob refers to the Jew when his service of G‑d requires toil, struggle and effort ("servants"), whereas Israel refers to the Jew when his service of G‑d is pleasurable and natural ("children").
Click here to read an article which discusses the "properties" of each name, and explains why the Torah chooses to refer to the Jews specifically by one name or another in various instances.
Rabbi Baruch S. Davidson