What is the biblical basis for concluding that God knows (in any sense) individual people personally (in any sense)?
God created you, so for sure he knows you! God is also watching each one of us and he loves ❤ us. And yes, there are quotations, to be sure!
For he looks to the ends of the earth and sees everything under the heavens.
1 John 3:19-20
By this we shall know that we are of the truth and reassure our heart before him; for whenever our heart condemns us, God is greater than our heart, and he knows everything.
And no creature is hidden from his sight, but all are naked and exposed to the eyes of him to whom we must give account.
But even the hairs of your head are all numbered.
There are many more, but these are what I could remember!
God, being the source of all intelligibility of creation, by His nature is all knowledgeable. Although many theists might view God as an 'impersonal force' of some kind, similar to the 'Force' in Star Wars, God is in fact not only personal, but more personal than we could ever imagine. This is due to God's omniscience. We are created in His image, and all that we think and know is founded in God's complete knowledge. This knowledge extends naturally to His creation, as does His love. A few biblical verses supporting this notion include the following;
For I know the plans I have for you, plans for welfare and not for evil, to give you a future and a hope.
For it is God who works in you, both to will and to work for His good pleasure.
My sheep hear my voice, and I know them, and they follow me.
1 John 4:10
In this is love, not that we have loved God, but that He loved us.
All of these verses, and plenty more if you simply read the bible, indicate both the Lord's full knowledge and full love of not only a collective people but of each and every person.
Read Psalm 139. God knows everything about you
O Lord, You have searched me and known me.
You know my sitting down and my rising up; You understand my thought afar off.
You comprehend my path and my lying down, And are acquainted with all my ways.
For there is not a word on my tongue, But behold, O Lord, You know it altogether.
You have hedged me behind and before, And laid Your hand upon me.
For You formed my inward parts; You covered me in my mother’s womb.
I will praise You, for I am fearfully and wonderfully made; Marvelous are Your works, And that my soul knows very well.
My frame was not hidden from You, When I was made in secret, And skillfully wrought in the lowest parts of the earth.
Your eyes saw my substance, being yet unformed. And in Your book they all were written, The days fashioned for me, When as yet there were none of them.
How precious also are Your thoughts to me, O God! How great is the sum of them! If I should count them, they would be more in number than the sand; When I awake, I am still with You.
God knows each and every one of us personally. Our entire purpose in this life, yea the key to eternal life is to ultimately reciprocate that- to come to Know Him and His Son. Consider John 17:3 , Acts 17:27.
God is Omniscient, or "all knowing." He knows all things- 1 John 3:20, and His understanding is unsearchable Isaiah 40:28 (literally "there is no investigation of his understanding")
He knows us so well that he has even the hairs of our head numbered- Luke 12:7. What's interesting about the way that this is written is that it suggests not just that God knows how many hairs are on your head, but that he NUMBERED them, as in, God could accurately say, "Looks like he just lost hair number 789."
God told Jeremiah that before He formed him in the womb, He knew him, (Jeremiah 1:5). Interestingly enough, the word used isn't just "know" in the casual sense. It denotes intimacy, friendship. It also renders as past tense- Imagine that! Before we are born, God can say that He already KNEW us! We are not a surprise to God, our arrival into this world is well known to Him- and shall I even begin to talk about Ephesians 1:5?
God knows everything we will do, would do, could do, should do... nothing escapes His notice or knowledge. (see Proverbs 15:3) He sees us for who we are, and what we could be and will be, all at the same time.
Referring back to Acts 17, referenced earlier, it becomes clear that God is a strategic God. He knows when and where you will be born, and it is deliberate and purposeful. "From one man he made all the nations, that they should inhabit the whole earth; and he marked out their appointed times in history and the boundaries of their lands. God did this so that they would seek him and perhaps reach out for him and find him..." Acts 17:26-27a
Never forget that it is God's will for everyone to be saved, 2 Peter 3:9 (unfortunately, not everyone wants that for themselves). Now does that sound like a God that doesn't know you? One that prioritized your salvation before the foundation of the world? (1 Peter 1:20, Revelation 13:8)
Someone once said that they didn't believe in God because if there was a God, such a being would be too busy for the minutiae of their life- but isn't that exactly the kind of God you would want?! And it is the kind of God that we have, so much so that David looked at himself in comparison to the moon and the vast stars and was humbled by the the fact that God cares about man.
"When I consider thy heavens, the work of thy fingers, the moon and the stars, which thou hast ordained; 4 What is man, that thou art mindful of him? Psalm 8:3-4a
SUCH A GOOD QUESTION. Frankly, a book could be written on the subject. I realize my answer was charged with a lot of emotion and probably wasn't the usual blunt theology of this forum, but I hope I helped, and, of course, if you need more of a didactic explanation, I'm happy to supply it- I just tend to be more on the Proverbs 15:23 side of things:
"A man finds joy in giving an apt reply-- and how good is a timely word!"
Then hear thou in heaven thy dwelling place, and forgive, and do, and give to every man according to his ways, whose heart thou knowest; (for thou, even thou only, knowest the hearts of all the children of men;) - 1 Kings 8:39 KJV