It appears to have started to become popular during the “early modern” period (period of the early Achronim), probably due to a boom in the population. That way “Yaakov Yisrael” can be distinguished from all the other babies named “Yaakov ….”.
One should note that the doubling of the Hebrew name with a name in the local language goes back to ancient times, such as “Yaakov Yisrael” being known also as “James Israel” when he goes out among the goyim.