Praise be to Allah.

Firstly: 

‘Eesa ibn Maryam (Jesus son of Mary – peace be upon him) is one of the Messengers of strong will. Allah sent him to the Children of Israel, and taught him the Torah and the Gospel. He stated that he came to confirm what was in the Torah, affirming it and believing in it, but he abrogated some of its rulings. He spoke Hebrew, the language of the Children of Israel. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:

Undoubtedly the people of Moosa (peace be upon him) were the Children of Israel, and the Torah was revealed in their language. Similarly the Children of Israel were the people of the Messiah (peace be upon him), and the Messiah spoke their language. Neither of these two Messengers addressed anyone except in the Hebrew language, and neither of them spoke Latin, Syriac, Greek or Coptic. End Quote.

Al-Jawaab as-Saheeh (2/94) 

He also said:

It is well-known according to the consensus of the Christians that the Messiah did not speak anything but Hebrew, like all the Prophets of the Children of Israel, and he used to pray facing towards their qiblah (direction faced during prayer). He did not pray facing towards the east and he did not instruct people to pray facing towards the east. End quote. 

Al-Jawaab as-Saheeh (3/32) 

Secondly: 

The [Arab] Christians call the Prophet of Allah ‘Eesaa Yasoo‘; in Hebrew the name is Yeshua. This is a name that is composed of two words, Yahweh Shu‘, meaning saviour. This name was common among the Israelite tribes, such as Yashoo‘ ibn Noon (Yeshua ben Nun – Joshua son of Nun) and Yoosha‘ the servant of Moosaa (peace be upon him), who became a Prophet after him (peace be upon him).

Shaykh Rasheed Rida (may Allah have mercy on him) said: 

The name ‘Eesa is an Arabised form of the name Yashoo‘ (Yeshua), with a transposition of letters, altering the letter sheen to seen. This often happens in words that are transmitted from Hebrew to Arabic. The letter seen in the words al-maseeh (messiah) and Moosa is a sheen in Hebrew (mashiach and Moshe), as is the final letter in the word shams (sun, which in Hebrew is shemesh). End quote. 

Tafseer al-Manaar (3/251) 

Al-Qaasimi (may Allah have mercy on him) said: 

‘Eesa is the Arabised form of the name Yasoo‘, which is a Greek word meaning saviour; it is the same as the name Yashoo‘ (Yeshua), except that the latter is Hebrew . End quote. 

Tafseer al-Qaasimi (2/318) 

Ash-Shawkaani (may Allah have mercy on him) said: 

There is a difference of opinion concerning the origin of the word maseeh (messiah). It was said that it comes from the word mas-h because he wandered (masaha) in the land, i.e., he travelled in it and never settled in any one place. And it was said that he did not touch (yamsah) any afflicted person but he was healed, therefore he was called maseeh (one who touches). According to these two views, the word is an active participle. And it was said that it is because he anointed himself (yamsah) with the oil with which the Prophets anointed themselves. And it was said that it is because the bottom of his feet was flat (mamsooh); or because beauty touched him (masahahu); or because he was anointed (musiha) by purification from sin. According to these four suggestions, the word is a passive participle. 

Abu’l-Haytham said: The maseeh (Messiah) is the opposite of al-maseekh. Ibn al-A‘raabi said: The maseeh is the siddeeq (strong and true in faith). 

Abu ‘Ubayd said: The origin of this word in Hebrew is mashiach, which was Arabised, as the name Moshe was Arabised to Moosa. 

‘Eesa is a non-Arabic name; it was also suggested that it is an Arabic name, derived from the verb ‘aasahu/ya‘oosuhu, meaning he managed his affairs. 

It says in al-Kashshaaf: It is an Arabised form of the name Ayshoo‘. End quote. 

What we see in the Gospel, in several places, is that his name is Yashoo‘ (Yeshua). End quote. 

Fath al-Qadeer (1/391) 

Ibn ‘Ashoor (may Allah have mercy on him) said: 

The Children of Israel used to call him Yashoo‘ an-Naasiri or an-Nasri (Jesus the Nazarene, or Jesus of Nazareth). End quote. 

At-Tahreer wa’t-Tanweer (1/533) 

It says in the Gospel of John: 

³ So Judas came to the garden, guiding a detachment of soldiers and some officials from the chief priests and the Pharisees. They were carrying torches, lanterns and weapons.

⁴ Jesus, knowing all that was going to happen to him, went out and asked them, “Who is it you want?”

⁵ “Jesus of Nazareth,” they replied.

“I am he,” Jesus said.

(John 18:3-5 – New International Version) 

So the Messiah (peace be upon him) was known among all the Jews and the Children of Israel as Jesus of Nazareth, named after the city of that name. 

They also mentioned that the word Messiah is a Jewish title mentioned in the Torah, that may refer to any Prophet, and every Jewish king was called a messiah. The meaning of the word is the one who is chosen by God, as was mentioned in Mark 8:29. In Psalms 105:15 the word is used to refer to all the prophets of God. 

According to the Jews, the name Yashoo‘ (Yeshua) means the one who is chosen by the Lord; the saviour. But they did not believe in ‘Eesa (peace be upon him); rather they tried to kill him and get rid of him, but Allah saved him from them and took him up to Him. 

Thirdly: 

The name of the Messiah (peace be upon him) in the Qur’an is ‘Eesa, which is an Arabised form of the Hebrew name Yashoo‘ (Yeshua), as the Qur’an was revealed in Arabic. In fact there is no difference between the two names, because when non-Arabic names are Arabised, they go through some changes.