The first time "Christ" is used in the Bible is Matthew 1.1,

"The book of the generation of Jesus Christ, the son of David, the son of Abraham".

Christ = "anointed". Christ was the Messiah, the Son of God. You can say Jesus Anointed or Jesus Messiah, Son of God, who is Jesus Christ in name. His name is descriptive, but nonetheless, His name is still true. Just because the name is descriptive does not discount the name. Christ is not an appellative, but the revealed name of the 2nd Person of the Godhead. This is revealed not in the head, but in the spirit of man as the Holy Spirit came upon men and entered into the spirit of men by the Holy Spirit. When I say man here, of course I mean both men and women, for God He made man, he made him, both male and female (Gen. 1.26). Before the foundations of the world the 2nd Person of the Godhead was Jesus Christ. He reveals Himself to us as Jesus Christ, his name. Which came first our knowledge of His name, or the Son of God having this name? The latter.

Jesus is the Christ. This is not like saying Benedict the Pope, since the Pope did not resurrect himself. But Jesus, being God, as the Christ did rise from Hades on the 3rd day of His own volition. Pope doesn't refer to resurrection, but a man who is a leader of the great harlot of "religious Rome" (Rev. 17) "because she made all nations drink of the wine of the wrath of her fornication" (Rev. 14.8). Since we see Matt. 1.1 show us a name, it is a name, which therefore, is your misreading of the Greek.

Grammar is fully capable of expressing the descriptiveness of the name as well as the name for God gave both the grammar to know the name and ability to be descriptive. Christ is One Person of the Godhead. He is not interchanged with the Father or the Son. The name of Christ nor His description is an appellative since His name existed before the foundations of the world. Grammar can splice between the descriptiveness of words and the name of the Son of God, Jesus Christ. We are able to do so by the Holy Spirit.

We do not have the one Christ who was named Jesus, but the name of the Son of God is Jesus Christ. Jesus is named the Christ because He is Jesus on earth, Christ in resurrection.

Christ is the last name of Jesus. Which is His authority to the fact as you state, they used patronymics, and yet this was His name quite contrary to the practice, because He is God.

The reason Jesus is from Nazareth is because He was prophesied, "And he came and dwelt in a city called Nazareth: that it might be fulfilled which was spoken by the prophets, He shall be called a Nazarene"(Matt. 2.2). You're getting your causes and effects mixed up when you said the only reason He was called a Nazarene was because He was the only famous one there. You don't know the Bible, trying to read it by your corrupted intellect, which as we have seen is flawed each time. This is not merely a good enough identifier but the fulfilment of God's providence.

Jesus wanted us to know His last name was Christ. Remember, this can not be known to you, "interpreting spiritual truths to those who possess the Spirit" (1 Cor. 2.13), because you are without the Spirit of the Father and the Son. God has not let you know Him to know the name of His Son. Your spirit needs to be regenerated by the Holy Spirit to receive God's uncreated life. Only then shall you not go to perdition, an eternal separation from God.

"Now the birth of Jesus Christ was on this wise" (Matt. 1.18).