You asked: Is God really defined by your faith?
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In my view, of course not. God is who God is. We are trying to learn just who God is, and what He is like. Faith is our belief about those things. We cannot define God, any more than we can choose the attributes of a lemon. If we “believe” a lemon is sweet, does it become sweet? The same with God. What we believe does not define God. We just hope and believe that what we believe about God is correct.
When you talked about God being something other than what your faith defined, that is what I thought you meant.
Please replace defined with allowed in my last.