What binds the three traditions to Abraham is not a biography but a covenant, and each marks its claim on him with a title of its own.
In Genesis the covenant is the spine of the story: a promise of land and of descendants, sealed by circumcision as its sign, and reckoned to Abraham as righteousness because he believed it before any law was given. Judaism knows him as Avraham Avinu, Abraham our father, first of the patriarchs and, in later tradition, the first to recognise one God amid idolatry.
Christianity, following Paul, made that pre-legal faith the model of justification: Abraham was counted righteous by trust, not by works of the law, which let Paul argue that Gentiles who share his faith are his children without becoming Jews first. He is the father of all who believe.
Islam calls him Ibrahim and gives him two titles that state his standing: Khalil Allah, the friend of God, from the Quran's statement that God took Abraham as a friend, and hanif, one of pure, original monotheism who, the Quran insists, was neither Jew nor Christian but one who submitted to God, so that the primordial faith is traced through him. The profession of the millat Ibrahim, the creed of Abraham, makes him not a shared ancestor at the edge of the story but its pattern.
Three founders' faiths, then, hold the same man as the point where right worship begins, and locate the start of their own distinctiveness in what they say he was.