Around the time of the Exodus, the Jewish people were known as "Hebrews", certainly as individuals. (Take a look at some Ellis Island records and you'll see a lot of people listing their nationality as "Hebrew, Polish"). As a whole they become known as "Bnai Yisrael." Similarly, Joseph is described as a Hebrew, and Jonah introduces himself as such as well.
It's several hundred years later, when the southern kingdom of Judea is the remaining one, that individual Jews become known as "Yehudim", technically "Judeans." Thus Mordechai in the Megillah is a "Yehudi", generic for "Jew" (as we say in English today, "Juda-ism"), though his actual tribe of ancestry was Benjamin.
The term "Yisrael" to refer to an individual Jew -- "he is a Yisrael" -- much later, Talmudic terminology.