This article investigates difficulties in defining the concept of God by focusing on the question of what it means to understand God as a ‘person.’ This question is explored with respect to the work of Søren Kierkegaard, in dialogue with Franz Rosenzweig, Martin Buber, and Emmanuel Levinas. Thereby, the following three questions regarding divine ‘personhood’ come into view: First, how can God be a partner of dialogue if he at the same time remains unknown and unthinkable, a limit-concept of understanding? Second, if God is love in person and at the same time a spiritual reality ‘between’ human agents, in what ways are his personal and trans-personal traits related to each other? Third, what exactly is revealed through God’s ‘name’? By way of an inconclusive conclusion, divine personhood is discussed in regard to prayer, where the problems of predication that arise in third-personal speech about God are linked with the second-personal encounter with God.