What is the Biblical definition of what makes one a Christian?

A true Christian is a person that is baptized by the Holy Spirit (Mark 16:16). The confusion is created because few actually know what this means. To build a proof that one is indeed baptized by the Holy Spirit an outlined structure first needs explained.

Phase One: Peace with God without the Knowledge of Good and Evil (Gen 1:31).

Phase Two: Abel dies to Cain because Cain Knew it was good to have Gods approval and became angry (Gen 4:5).

Phase Three: God floods the world because every thought of the human heart was evil (Gen 6:5).

Phase Four: The Law was written to describe actions that would prevent anger.

Phase Five: Natural rebellion against the laws.

Phase Six: Jesus shows that by faith God can protect the self from getting angry.

Phase Seven: Resurrect for himself a crop of humans that do not get angry, and peacefully live for all eternity.

Anger and Love, these are moods / attitudes / your spirit. From an ancient Jewish perspective, if I were to Jerry-Rig something I would be doing it in the name of Jerry. Therefore, those that through faith can prevent themselves from becoming angry, and can resist the physical urges that make others angry, or distract themselves from thoughts given from God. These are the ones that are baptized into his name (Romans 2:14-15).

The Wheel of Emotions: Denial - Anger - Bargaining - Depression - Acceptance
In Jesus Terms: Lack of Faith - Gnashing of Teeth - Weeping - Forgiveness

Wear the clothes: (Ephesians 4:22-24 Romans 13:14) Because if Not: (Matthew 22:1-14)

If you can separate your evil thoughts from your good thoughts, and believe that God's angels will gather the bad thought and throw them in the fire (Matt 13:30), instead of releasing them with your mouth, only to have more evil return (Luke 11:24). Then your Demons have been taken away from you by the Power of God, and you can know that you have found Heaven (Luke 11:20). Seek Heaven First (Matthew 6:33). Welcome to the family.

The word Christian was coined to mean little Christ in Antioch:

Act 11:25 and 26

25 Then departed Barnabas to Tarsus, for to seek Saul:

26 And when he had found him, he brought him unto Antioch. And it came to pass, that a whole year they assembled themselves with the church, and taught much people. And the disciples were called Christians first in Antioch.

This was attached to the disciples there and spread as a description of what was formerly known as 'people of the way', that title was attached to the followers of Jesus while they were still attending the Tabernacle of God, or the Jewish Synagogue, as a way of differentiating them from the Judaist.

When they began to be persecuted by the Sanhedrin and forced out of the Synagogue, they began to meet in houses of the believers in Jesus.

That term slowly evolved into Christians and was strictly applied to Disciples of Jesus everywhere.

That having been said if there is a strict definition as far as the Bible goes it would have to depend upon that given in Acts since that is where and for whom the term was coined.

In John 3:3-6, Jesus explains salvation to Nicodemus,

Jesus answered him, “Truly, truly, I say to you, unless one is born again he cannot see the kingdom of God.”

Nicodemus said to him, “How can a man be born when he is old? Can he enter a second time into his mother's womb and be born?”

Jesus answered, “Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God. That which is born of the flesh is flesh, and that which is born of the Spirit is spirit.

In 1 John 2:3-11, John gives these guidelines for distinguishing Christians from non-Christians:

We know that we have come to know him if we keep his commands. Whoever says, “I know him,” but does not do what he commands is a liar, and the truth is not in that person. But if anyone obeys his word, love for God is truly made complete in them. This is how we know we are in him: Whoever claims to live in him must live as Jesus did.

Dear friends, I am not writing you a new command but an old one, which you have had since the beginning. This old command is the message you have heard. Yet I am writing you a new command; its truth is seen in him and in you, because the darkness is passing and the true light is already shining.

Anyone who claims to be in the light but hates a brother or sister is still in the darkness. Anyone who loves their brother and sister lives in the light, and there is nothing in them to make them stumble. But anyone who hates a brother or sister is in the darkness and walks around in the darkness. They do not know where they are going, because the darkness has blinded them.

Combining these together, we learn that a Christian is born again of the Holy Spirit, obeys they teaching of Jesus, and loves other Christians.

1 John continues with other requirements, such as not loving the world in 1 John 2:15-17:

Do not love the world or the things in the world. If anyone loves the world, the love of the Father is not in him. For all that is in the world—the desires of the flesh and the desires of the eyes and pride of life—is not from the Father but is from the world. And the world is passing away along with its desires, but whoever does the will of God abides forever.

Meanwhile, 1 John 2:22-23, states that they cannot deny that Jesus is the Christ, but confess him:

Who is the liar but he who denies that Jesus is the Christ? This is the antichrist, he who denies the Father and the Son. No one who denies the Son has the Father. Whoever confesses the Son has the Father also.

The Bible has no definition for who is a Christian.

The term 'Christian' was first used in Antioch in the first century. It is more likely that the people in Antioch called the followers of the new faith as 'Christians' to identify them. The Greek word Χριστιανός (Christianos) simply means "follower of Christ". The term was created by pagans and it has no bearing of Biblical meaning. As per the meaning of the secular term, 'Christian' would include anyone who professed to follow Jesus Christ.

and when he found him, he brought him to Antioch. So for a whole year Barnabas and Saul met with the church and taught great numbers of people. The disciples were called Christians first at Antioch. (Acts 11:26, NIV)

The Bible only gives the definition of sin and salvation. Jesus Christ did not use the term 'Christian'. Jesus did not come to introduce a new religion. Jesus came to save us, to die for our sins, to open the way to Heaven and to bring us to the Father. The New Testament gives the definition of what is sin and what is death. The Bible tells us why we suffer, why we die, why we are sinners, why we can't save ourselves and how God provided the way of escape from sin and it's punishment.

If Christian means "follower of Christ", here is what Jesus said to who ever wants to follow Him.

Then Jesus said to his disciples, “Whoever wants to be my disciple must deny themselves and take up their cross and follow me. (Matthew 16:24, NIV)

Matthew Henry commented on this verse.

A true disciple of Christ is one that does follow him in duty, and shall follow him to glory. He is one that walks in the same way Christ walked in, is led by his Spirit, and treads in his steps, whithersoever he goes. Let him deny himself. If self-denial be a hard lesson, it is no more than what our Master learned and practised, to redeem us, and to teach us. Let him take up his cross. The cross is here put for every trouble that befalls us. We are apt to think we could bear another's cross better than our own; but that is best which is appointed us, and we ought to make the best of it. We must not by our rashness and folly pull crosses down upon our own heads, but must take them up when they are in our way. If any man will have the name and credit of a disciple, let him follow Christ in the work and duty of a disciple.