At Bethlehem Baptist Church and at Desiring God we use the term “God-centered” a lot. Here is one simple way to tell what we mean and test yourself to see if you are God-centered.
The psalmist describes the motivation of God in saving sinners like this:
Both we and our fathers have sinned... Yet he saved them for his name’s sake, that he might make known his mighty power. (Psalms 106:6, 8)
God was motivated to rescue them and us from our sin and its penalty “for his name’s sake.” What does “for his name’s sake” mean? It means “that he might make known his mighty power.”
What we mean when we say God is “God-centered” is that he acts like that. He saves for the sake of his name. He saves to make known his own power.
And what we mean when we say we are God-centered (or desire to be) is that we like to have it that way. It satisfies us to have God save us for God’s sake. We are happy that this is the way it is. We get pleasure in seeing it and savoring it.
We like to talk about God doing it that way.