(He is) Most Kind (Lord) Who established (His sovereignty) on the Throne (of power and supreme authority over all the systems of the universe, befitting His Glory)
Rahman is established on the Throne (Rahman established His sovereignty by creating the worlds [the existential world created by the potential of the Names inherent in one’s brain] with His Names, i.e., in the quantum potential, Rahman observes His knowledge through His knowledge).
Sayyed Abbas Sadr-Ameli
The Beneficent (Allah Who) dominates on the 'Arsh (the Throne of existence)
Al-muntakhab fi tafsir al-Qur'an al-Karim
AL-Rahman Who set Himself on the Throne of supremacy and dominion , of grace and mercy