Being 'known by Jesus' in Matthew 7:22

Well, yes, you have answered it yourself.

"Know" here means known and loved.

"The 'knower' has actual involvement with or in the object of the knowing" - ("Vine's Complete Expository Dictionary" under the Hebrew entry "To Know").

And so "Adam knew Eve his wife, and she conceived..." (Gen 4:1) where intimacy is intended.

It is the same sense of intimacy as in Psalm 1v6 :

For the LORD knows the way of the righteous; but the way of the ungodly shall perish.

So, in Exodus 6:3 it is clear the word "know" does not merely mean what English means: I appeared to Abraham, and to Isaac and to Jacob, by the name of God Almighty, but by my name Jehovah (i.e. LORD, the tetragrammaton) was I not known to them. But actually they did know his name if we use the English sense of the word "know"(eg Genesis 14:22):

Yada' (3045 in Strong's) in the intensive and causative stems is used to express a particular concept of revelation. God did not make himself known by His name Jehovah to Abraham, Isaac, and Jacob. He did reveal that name to them, that He was the God of the covenant. Nevertheless, the covenant was not fulfilled (they did not possess the Promised Land) until the time of Moses. The statement in Exod 6:3 implies that now God was going to make Himself known "by His name"; He was going to lead them to possess the land. (Vine's)

The bare knowledge of His name Yahweh/Jehovah did not constitute a knowledge of Him by His covenant name. What was needed was a personal felt experience of all that the name means by going in to possess the land of promised in the covenant. Hence to know includes to know experientially.

Again from Vine's, it may also mean "to know by deduction" or "to know by observing and reflecting" rather than experience. Hence, Noah "knew" the waters had abated when he saw the olive leaf in the dove's mouth (Genesis 8:11). He could not see or experience the abated waters for himself, but he "knew" by deduction.

Returning to Matthew 7v22,23 (See Spurgeon's Sermon Notes, Kregel Publications, 1990):-

These open professors of religion attended to marvels, but not to essentials; they prophesied, but did not pray; they cast out devils, but the devil was not cast out of them; they wrought wonders, but were also workers of iniquity. Jesus had been omitted from their religion; they were utter strangers to his heart. He had neither chosen them, nor communed with them, nor approved them, nor cared for them.

Outwardly they looked good to others:

they were religious and undertook Christian service; they said "Lord, Lord"; they were energetic; they did everything in the name of Christ;

But they had no real faith in Jesus as their Lord and Saviour. Some currency is counterfeit. Some gold is Fool's Gold. Not all in the church are of the church (2 Timothy 2:19).

As if to say "I knew you well enough for "black sheep" or rather for reprobate goats: I knew you for hirelings and hypocrites, but I never knew you with a special knowledge of love, delight, and complacency. I never acknowledged, approved, or accepted of your persons or performances.

Notice, it was not "I once knew you but I cannot own you now"; but "I never knew you; - I never knew you as real penitents, as supplicants for pardon, as humble believers, or as true followers."

Perhaps they thought their works would make them accepted; but we must come to Jesus as sinners seeking for a free pardon, not as workers for our wages.

Those who accept His invitation "Come unto Me" (Matt 11:28) shall never hear Him say "Depart from Me". (Spurgeon)

Before attempting to live for Jesus we must believe on and entirely depend on Jesus and his finished work, I mean his blood and righteousness, for our justification, and on his Spirit for our sanctification.

For Jesus to ‘know’ us means we have submitted to his Lordship and we are no longer slaves but are intimate acquaintances. Jesus said this of his disciples:

Whoever does God’s will is my brother and sister and mother (Mark 3:35).

When we know Jesus and believe in him, we are adopted into God’s family:

Yet to all who received him, to those who believed in his name, he gave the right to become children of God (John 1:12)

We can call God “Abba, Father” (Romans 8:15). It doesn’t get more personal and intimate than that! When people speak of “knowing” Jesus, they refer to having a relationship with Him. Being a Christian is more than knowing about Jesus; being a Christian is about knowing Him personally. Jesus spoke of the need to know the Saviour when He prayed:

This is eternal life: that they know you, the only true God, and Jesus Christ, whom you have sent” (John 17:3).

When we know Jesus, we also know God:

We know also that the Son of God has come and has given us understanding, so that we may know him who is true. And we are in him who is true – even in his son, Jesus Christ. He is the true God and eternal life. (1 John 5:20)

There were people in Jesus’ day who thought they were friends of his because they knew the Law, made strict rules for themselves (and for others), and listened to his teaching. They followed him, applauded the miracles, and liked some of what he said. But Jesus calls them “evildoers” and declared, “I never knew you.” Matthew 7:21-23

They didn’t know who Jesus REALLY was. Some people have an intellectual, head knowledge of Jesus. They may have read the Bible and believe it, but have never allowed the truth about Jesus to penetrate into their hearts so that their lives are transformed. Jesus said:

These people honour me with their lips, but their hearts are far from me. They worship me in vain; their teachings are but rules taught by men. (Matthew 15:8–9 quoting Isaiah 29:13)

To really know Jesus means we grasp the significance of what God, in Jesus, did to pay for our sins and we seek his forgiveness so that we may know him personally, and enjoy intimate fellowship with him through the Holy Spirit (Acts 2:38).