The Greek language was first spread by Alexander the Great after he defeated the Persian Empire in 323 B.C. Because of Alexander’s conquest Greek became the major international language of their time period. Greek became the dominant language of Israel and the world at the time of Christ. God used this to reach out to the Gentiles that did not speak Aramaic or Hebrew.

The Old Testament was translated into the Greek language 250 plus years before Christ by the 70, Sanhedrin. This Greek translation was first done by Jews for Greek-speaking Jews in Alexandria Egypt. The Pentateuch was first translated, than later the rest of the Old Testament books were added to the translation.

Long before the time of Jesus, the Jews stopped using Hebrew as their everyday language and kept it for their religious services. They continued to read the scriptures in Hebrew in the temple, but not exclusively. Aramaic was used as their common tongue, however they lived among those who spoke Greek. All Jews in Jesus day spoke at at least 2-3 languages and the language of the day was Greek like english today- they wrote it to reach the whole world. There is every indication during New Testament times Jesus and the disciples were multi-lingual. When it came time for them to quote the Old Testament in the Greek written New Testament, they preferred quoting from the Greek Septuagint. For example in Romans 3 there is a large quotation from Ps. 14, where there are six whole verses in the apostle's quotation which are not found in the present Hebrew text, but are preserved in the Septuagint! (from Adam Clarke's Commentary)

The New Testament writers - the apostles quote the OT Greek Septuagint more then the masoretic text.

The existing biblical manuscripts (with the possible exception of Matthew) tend to follow the Septuagint translation, and not the Masoretic Hebrew.

The use of the Greek name Iesous (Jesus) for Joshua, (Yeshua) was common long before the birth of our Savior. It is found in the Greek Septuagint translation of the Hebrew Scripture. The form s identical in the Old Testament Greek Septuagint to that of the New Testament text. The book of Yahoshua (Joshua) in the Greek Septuagint is named Iseous naus in Greek, meaning Joshua Son of Nun. So it was the Hebrews themselves that used the Greek language before Jesus' time.

If you lived back then you would have called Jesus the Messiah- Iesous christos in Greek, and Yeshua ha Mashiach when speaking Hebrew. Jesus would respond to either of these names. The proof is found in the Scripture. The Romans would not actually pronounce his name in the Hebrew tongue, they would speak their own language when they spoke to Jesus?

 The disciples prayed together in Acts 1:24: “You, O Lord, (Kurious) who know the hearts of all,” (Acts 8:24, 5:14, also the Lord.) this is the word they used when they translated the tetragrammaton. This confirms that there is no requirement to speak his Hebrew name in prayer.