Elohim was the name of God for the Israelite (northern) tribes.
IHVH was the name of the God of the Judeans (southern tribe).
Since both religions were based on the belief in a single, Creator, God, the two traditions were knitted into one when the refugees of the northern kingdom were absorbed into Judea following the destruction of the northern kingdom by the Assyrians around 725 BCE, at the instruction of the Judean King Ezekiah.
Despite the Judean scribes’ best efforts, however, the ‘seam’ between the two traditions is still visible in the Hebrew Bible, in details such as the two versions of the story of Creation (Gen. 1, 2); the different homelands of Abraham (ancestral forefather of the Judeans) and Isaac (forefather of the Israelites), and the sketchy and unconvincing portrait of their relationship; the different religious centres (Jerusalem for the Judeans; Beit-El for the Israelites); and the profoundly different character of the Israelite ones (e.g. Elijah, Elisha) from that of their Judean counterparts (e.g. Gad, Nathan, Isaiah).
That said, the effort did pay off: most Jews and Israelis (and Gentiles, come to that) subscribe unquestioningly to the notion that Judea and Israel were always a single nation, with a single religion, and shared ancestry.