Question: 1) How much of a person’s identity is uniquely God-given, and how much is merely a combination of genes and environmental factors? Also, 2) how do we know that a human is not merely a highly sophisticated animal?
Response: These questions seem to imply that if we can fully explain a person based on DNA and environmental factors, we have no need for God. We know this is not true, for if God does not exist, then only matter exists, shaped by pure chemistry and physics. In such a world there would be no abstract thoughts such as the questions given in this post. In a purely material world, we would be the result of natural forces, never able to overcome the external forces that shapes us. But our experience and our reason tells us this is not true. (For longer explanations of this, see here and here and here. )
Further, the biggest assumption in the first question seems to be built upon an either/or fallacy, namely that personality is either given directly by God or it is genetic and environmental. Personality could very well be developed by God using genetics and environmental factors. Certainly a Biblical case could be made that God uses circumstances to develop a person’s character, test one’s faithfulness, and teach us that He is dependable and wise. Theologians refer to God’s providence, which is where He works out situations through circumstances to achieve His will and His purposes. So we are safe in concluding that God brings experiences into our lives to shape us.
But Christians are more than that. The New Testament tells us that we are regenerated, that “if any man be in Christ, he is a new creation: old things are passed away; behold, all things are become new.” (2 Corinthians 5:17). As new creatures in Christ we have new desires, new purposes, new goals. Many Christians can give testimony that the Bible is correct in that in the new birth, they have a change of direction, a new set of wants and desires.
How much is genes and environment versus direct intervention of God? The apostle Paul tells us even he had a struggle between the old and the new. Paul gives a vivid description in the last part of Romans 7. As Christians, we are both our old self and our new, awaiting the ultimate day when we are redeemed both in body and soul.
As to humans and animals, we know that humans are highly sophisticated animals. The point is that we are not merely and only sophisticated animals. We are told this in the Bible when it says that we are created in the image of God. Animals follow instinct and do not have control over their passions without external training by people. As Vernon McGee once said, if we ever see a monkey on his knees in repentance, then we can take them more seriously as compared to humans.