Ismail is also the name of the son of Prophet Ibrahim. In the Kur'an, Ibrahim asks Allah for a son and promises to sacrifice him. Just as he sacrifices Ismail, Allah sends Cebrail and tells him that this was a test and that he passed it. The father and son later built Kabe together. This hints to the character Ismail's relationship with authority in this film.
Beybaba is a name used by children when referring to their fathers. The word is composed of two words; "Bey" and "Baba". Baba means father, and bey is a word used while respectably referring to men in Turkish.