My husband and I first became acquainted with the principle of family identity in the 1900's, when we were asked to teach a class on biblical parenting. It is blessing to many young families, I only wish we knew about it when we are raising our girls.
Family identity birthed at a young age will give a child security, purpose and a healthy self image. It will help to separate your family from other families. For instance, when your son or daughter comes to you and tries convince you that all their friends are "going to a party that you disapprove of, you can respond to the manipulation by saying, " But, we (your surname) don't go to those kind of parties." If you clearly can give a biblical explanation, it will really helps your child to submit to your authority as unto the Lord.
If family identity is established early in an earthly family, how about God's eternal family? I believe this concept can be translated into the family of God. We have a new family identity. Jesus being our elder brother shows us the love of our spiritual "daddy", Father God.
One of the greatest works of the Holy Spirit is to establish us as children of God in His Kingdom. We are different then the world. 1John 3:9 says it this way, "No one born of God makes a practice of sinning . For God's SEED ABIDES in him and he cannot KEEP on sinning because he has been born of God. By this it is evident who are the children of the devil. Whoever does not practice righteousness is not of God, nor is the one who does not love his brother." This does not mean that we are prefect and never sin, but it does mean we want to obey God.
We have a new identity created in the image of Christ. Daily we are dying to the old self life. Our minds are renewed and growing to accept God ways as our new identity.
2 Peter 3,4 says, " His divine power has granted to us all things that pertain to life and godliness, through the knowledge of Him, who called us to his own glory and excellence, by which He has granted to us His precious and very great promises, so that through them you may become PARTAKERS OF THE DIVINE NATURE , having escaped from the corruption that is in the world because of sinful desire......." We are in the world , but not of it. The spirit of this world is no longer our identity. Our flesh, (lower nature) is NOT WHO WE ARE.
We have a new family identity in Jesus Christ. We are sojourners, ambassadors on earth, to proclaim the gospel, and MUCH MORE, until our work on earth is finished and the Lord calls us to our eternal home.