What is the name that is big enough to hold your life?

How about 'Child of the Father'?

To be a Christian is to believe that it is the Father who defines our identity and is to be believed against all inner and outer accusations to the contrary when he says to us, “This son of mine”. To know that is not to skulk in the back pew; it is to come forward with confidence to receive the inheritance. The robe which is the garment of sonship is accompanied by the ring which is the insignia of authority and the sandals that distinguish the free man from the slave. The son who comes home is invited back into his lost inheritance, to delight again in his father’s company and goodness and to rejoice. Thomas Smail

Romans 8:9-17
But if God himself has taken up residence in your life, you can hardly be thinking more of yourself than of him. Anyone, of course, who has not welcomed this invisible but clearly present God, the Spirit of Christ, won't know what we're talking about. But for you who welcome him, in whom he dwells—even though you still experience all the limitations of sin—you yourself experience life on God's terms. It stands to reason, doesn't it, that if the alive-and-present God who raised Jesus from the dead moves into your life, he'll do the same thing in you that he did in Jesus, bringing you alive to himself? When God lives and breathes in you (and he does, as surely as he did in Jesus), you are delivered from that dead life. With his Spirit living in you, your body will be as alive as Christ's!

So don't you see that we don't owe this old do-it-yourself life one red cent. There's nothing in it for us, nothing at all. The best thing to do is give it a decent burial and get on with your new life. God's Spirit beckons. There are things to do and places to go!

This resurrection life you received from God is not a timid, grave-tending life. It's adventurously expectant, greeting God with a childlike "What's next, Papa?" God's Spirit touches our spirits and confirms who we really are. We know who he is, and we know who we are: Father and children. And we know we are going to get what's coming to us—an unbelievable inheritance! We go through exactly what Christ goes through. If we go through the hard times with him, then we're certainly going to go through the good times with him!