That is an excellent question.
The Old Testament actually refers to Jesus many times, although not by that exact name. The Old Testament (old covenant) between God and Man was for man to offer God a sacrifice each year for his individual sins. That sacrifice was to be a blemish-free lamb which was to be burnt by the High Priest. Those who kept that law had their sins forgiven. The Israelites also had the prophets to proclaim the Word of God to them on a regular basis, and there are clear examples of forward-looking recognition that the Son of God was their salvation.*
It is noteworthy that the Jews ultimately rejected and even murdered the prophets for hundreds of years, which led to the nation of Israel's almost constant state of captivity as punishment by God. In fact, at the time that Jesus was born, Rome had conquered Israel and was ruling the country with a firm hand. The spiritual leaders of the nation were allowed to continue to practice their religion, however, and they (the Pharisees) had a certain level of status under Roman occupation. It was into this climate of unbelief and religious arrogance that Jesus was born. When he became an adult, he began his ministry in which he preached repentance and judgment, especially for the Pharisees. But the thing they really couldn't stomach was that he claimed to be the Messiah. This threatened to upset their little cabal, so they conspired to kill him by inciting a mob and trumping up false charges of blasphemy.
*The Bible says there is only one God, but He is manifest in three Persons, the Father, the Son, and the Holy Spirit. Jesus Christ was God the Son.
The Bible says Jesus Christ is God. “Who says?” someone might ask. Following are some of those in the Bible who said that Jesus Christ is God.
DAVID CALLED HIM GOD
"Saying, What think ye of Christ? whose son is he? They say unto him, The son of David. He saith unto them, How then doth David in spirit call him Lord, saying, The Lord said unto my Lord, Sit thou on my right hand, till I make thine enemies thy footstool? If David then call him Lord, how is he his son?" (Matt. 22:42-45).
ISAIAH CALLED HIM GOD
"Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel" (Isaiah 7:14).
"For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace" (Isaiah 9:6).
JEREMIAH CALLED HIM GOD
"Behold, the days come, saith the LORD, that I will raise unto David a righteous Branch, and a King shall reign and prosper, and shall execute judgment and justice in the earth. In his days Judah shall be saved, and Israel shall dwell safely: and this is his name whereby he shall be called, THE LORD OUR RIGHTEOUSNESS" (Jeremiah 23:5-6).
MATTHEW CALLED HIM GOD
"Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us" (Matthew 1:23).
CHRIST CALLED HIMSELF GOD
"But Jesus answered them, My Father worketh hitherto, and I work. Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God" (John 5:17-18).
"Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. Then took they up stones to cast at him: but Jesus hid himself, and went out of the temple, going through the midst of them, and so passed by" (John 8:58,59).
"I and my Father are one. Then the Jews took up stones again to stone him. Jesus answered them, Many good works have I showed you from my Father; for which of those works do ye stone me? The Jews answered him, saying, For a good work we stone thee not; but for blasphemy; and because that thou, being a man, makest thyself God" (John 10:30-33).
"I am Alpha and Omega, the beginning and the ending, saith the Lord, which is, and which was, and which is to come, the Almighty" (Revelation 1:8).
THE ANGELS CALLED HIM GOD
"For unto you is born this day in the city of David a Saviour, which is Christ the Lord" (Luke 2:11).
THE BLIND MAN CALLED HIM GOD
"Jesus heard that they had cast him out; and when he had found him, he said unto him, Dost thou believe on the Son of God? He answered and said, Who is he, Lord, that I might believe on him? And Jesus said unto him, Thou hast both seen him, and it is he that talketh with thee. And he said, Lord, I believe. And he worshipped him" (John 9:35-38).
THOMAS CALLED HIM GOD
"And Thomas answered and said unto him, My Lord and my God" (John 20:28).
PETER CALLED HIM GOD
"Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons: But in every nation he that feareth him, and worketh righteousness, is accepted with him. The word which God sent unto the children of Israel, preaching peace by Jesus Christ: (he is Lord of all)" (Acts 10:34-36).
JOHN CALLED HIM GOD
"In the beginning was the Word, and the Word was with God, and the Word was God" (John 1:1).
"Hereby perceive we the love of God, because he laid down his life for us: and we ought to lay down our lives for the brethren" (1 John 3:16).
"And we know that the Son of God is come, and hath given us an understanding, that we may know him that is true, and we are in him that is true, even in his Son Jesus Christ. This is the true God, and eternal life" (1 John 5:18).
PAUL CALLED HIM GOD
"Take heed therefore unto yourselves, and to all the flock, over the which the Holy Ghost hath made you overseers, to feed the church of God, which he hath purchased with his own blood" (Acts 20:28).
"Let this mind be in you, which was also in Christ Jesus: Who, being in the form of God, thought it not robbery to be equal with God" (Philippians 2:5-6).
“Who is the image of the invisible God, the firstborn of every creature: For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers: all things were created by him, and for him: And he is before all things, and by him all things consist.” (Col. 1:15-17).
"And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory" (1 Timothy 3:16).
"Looking for that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ" (Titus 2:13).
GOD THE FATHER CALLED HIM GOD
"But unto the Son he saith, Thy throne, O God, is for ever and ever: a sceptre of righteousness is the sceptre of thy kingdom. Thou hast loved righteousness, and hated iniquity; therefore God, even thy God, hath anointed thee with the oil of gladness above thy fellows" (Hebrews 1:8-9).
Hebrews 1:8-9 is quoted from Psalm 45, and in Psalm 45 it is obvious that God the Father, Jehovah God, is speaking about the Son. God the Father calls the Son God, and God the Son calls the Father God. This is the mystery of the Trinity. Though we do not fully understand it, we believe it because it is the teaching of the Scriptures.