"But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his." (Romans 8:9)
To identify with someone as define by Webster contemporary dictionary is simply a feeling that you share and understand the problems or experiences of another person, the act of identifying with them.
One way by which God recognizes or identifies with his own, is by His Spirit indwelling them. Ephesians 1:13 says we have been sealed with the Holy Spirit since we believed. So, God knows you by your name and address. He sees you with His Spirit. 2 Timothy 2:19 says God knows those that are His, this He does by His Spirit in you.
There are two dimensions of the spirit of God upon man. There is the indwelling of God's Spirit and the infilling of the Spirit of God. The indwelling has to do with the Spirit residence in man. 1 Corinthians 6:19 says "Or do you not know that your body is the temple of the Holy Spirit who is in you, whom you have from God, and you are not your own?" Our body is God's temple, He lives in us.
The infilling experience is being filled with all that the Holy Spirit is. Apostle Paul said we should not be filled with wine wherein excess, but to be full of the Holy Spirit. It is possible to be born again, have the Spirit of God and then not be filled with the Holy Spirit. There is such a thing as being filled with the Holy Spirit. It is possible for a glass of water to be half filled or half emptied. But everyone would be aware if the glass of water is full.
Being filled with the Holy Spirit should be believers daily experience. Man actually is a spirit being. There is a formed man and there is a made man! Man was made in the image of God, and that is who we are. God is Spirit, and man is essentially a spirit being. Zechariah 12:1 tells us that God formed the spirit of man within him.
But in order for the spirit of man to find expression on earth, God formed the body of man from the dust of the earth. From here, we can deduce that man is not his body. The body is only a container that houses the spirit. Hebrews 12:9 tells us that God is the father of spirits. So, God identifies with you as a believer through your spirit by His Spirit. This is why it is always essential that your spirit is attuned with God's Spirit.