A few years after writing this, I revisited the subject here
by Rabbi Avi Billet
When I was studying in yeshiva, I recall asking one of the rabbis if there is a theme as to when the name Yaakov is used to describe the third patriarch, as opposed to when the name he was given later, Yisrael, is used.
The rabbi was of the opinion that the name Yisrael is used in a context that has national and historical significance, while Yaakov is used when referring to the specific family of the patriarch and their personal experiences.
This theory is nice, but on close examination it does not hold water.