I’m a growing fan of Derrida. Now this is not a presumptuous statement; as if to suggest I understand him. It’s just that as I delve more into his understanding of “religion”, I am coming to understand that in a simplistic sense, I agree with a lot of what he is saying. The following are a few quotes from his interview with Yvonne Sherwood and Kevin Hart, in Derrida and Religion: Other testaments.
…God is not some thing or some being to which I could refer by using the word “God.” The word “God” has an essential link to the possibility of being denied. On the one hand, God is far beyond any given existence; he has transcended any given form of being. So I cannot use the word “God,” I mention it. It is a word that I receive as a word with no visible experience or referent.
This comes back to what I said about prayer. When I pray, if I say “God,” if I address God, I don’t know if I am using or mentioning the word “God.” It is this limit of the pertinence of the distinction between mention and use which makes religion possible and which makes the reference to God possible… What are we doing when we name God? What are the limits of this naming? Now we know that in many Abrahamic traditions God is nameless, beyond the name. In Jewish traditions, God is the empty place, beyond any name. But we name the nameless. We name what is nameless. And when we name “what is not,” what is or is not nameless, what do we do?… To mention the word “God” is, in a certain way, already an act of faith. I’m not sure that there is pure faith, but if there is it would consist in asking the question, “When I use the word ‘God,’ am I referring to someone or mentioning a name?” (37-38)
What do I understand from this?
Well, keeping in my the principle of deconstruction; which simply put, begins by questioning the relationship between the word (language) and the referent (object), by stipulating that when we refer to a “glass” we are actually referring to a word “glass” or even the concept (again words) denoting “glass” rather than actually representing the actual glass… it thus makes sense to say that when we say God we don’t actually “have” God but refer to the word God.
And yet, through the act of faith, we believe that our use of the word “God” actually refers denotes God himself, and not just names God, but also “calls” him (another Derrida thought, later in the same interview).
In effect, Derrida is not questioning whether God exists, but questions our use of the word God and yet accords it much possibility when combined with faith in the nameless God who allows himself to be denoted (named) by our idioms, names.

I think you are on the right track, but you need to take it further. YOu got the first part right “to say that when we say God we don’t actually “have” God but refer to the word God. but also, you have to remember that God is transcendence– he is beyond our grasp of knowledge. We can never know God, just like we can never know an other (two words). Further, we can never know ourselves because if language is never fully present, and we can only know ourselves through language, well, then, we can never fully know ourselves because of the limitations of language.
I would like to see what else Derrida has to say here: ““When I use the word ‘God,’ am I referring to someone or mentioning a name?” It cant be that I refer to someone because God is not a “someone”, so we are refering to a name with no referent.
interesting stuff…