EDIT I am aware that Ibrahim is a variation on the name Abraham. My question specifically refers to the history of Islam itself, not before the prophet Mohammed received his revelations.
His real name is actually Ibrahim, so any significance to the name is irrelevant. However, his nom de guerre, Abu Bakr Al Baghdadi, is quite significant, since Abu Bakr was one the earliest converts to Islam, a close friend and confident of the Prophet, and the first Caliph to lead the Muslims after the death of Mohammad.
Ibrahim = Abraham. Abraham is a major figure in both the Bible and the Koran, as both the Jewish and Arab races are descended from him (Arabs through his first son Ishmael, Jews through his second son Isaac).
Abraham is considered the second most important prophet in Islam and a symbol of pure monotheism. It is also a very common male name among Muslims as Muhammad named his son Ibrahim.