In his nature, God is ineffable to human mind. But the Church teaches that, in the "economy of our salvation" God revealed himself as three Hypostases, distinct and unconfused. In his nature, according to the Church teaching, God is a simple, indivisible monad.
In addition, the miracle of Incarnation resulted in the second Hypostasis of the Godhead taking on human nature, human soul and body, and becoming a man, while retaining his fully divine, eternal, uncircumscribed, greater than creation nature.
Furthermore, the Church teaches that the Father is without a cause. He eternally begets his Word and the Spirit eternally "effuses" or sprites from the Father and goes to the Son. As regards their existence, the Word (Son) and the Spirit proceeds form the Father and the Son is begotten of the Father.
However, the Hypostaese are co-equal, co-eternal and con-substantial (of same ineffable essence).
So, while the element of mystery (ineffable) is retained, the Church went into pretty detailed desxcription of the Triune God, none of which, of course is to be found in the Bible, but is derived from the "deposit of faith," believed "everywhere and always."
And how well does this detailed description work for you as far as helping "know exactly who we have that intimate relationship with, to know exaclty who that person is"?
I'd venture, not much. It's important for Church theology, but for the goal of knowledge sufficient for intimate relationship? I don't think so.
For me, ineffable means you're not going to get there in this manner -by detailed or exact definition, else God would be effable.