About 28 times. Below are the verses which contain the name Jesus. These have been taken from Abdullah Yusuf Ali's translation of the Holy Quran by running the a search of the word "Jesus" at www.al-quran.info
[2:87] We gave Moses the Book and followed him up with a succession of messengers; We gave Jesus the son of Mary Clear (Signs) and strengthened him with the holy spirit. Is it that whenever there comes to you a messenger with what ye yourselves desire not, ye are puffed up with pride?- Some ye called impostors, and others ye slay!
[2:136] Say ye: "We believe in Allah, and the revelation given to us, and to Abraham, Isma'il, Isaac, Jacob, and the Tribes, and that given to Moses andJesus, and that given to (all) prophets from their Lord: We make no difference between one and another of them: And we bow to Allah (in Islam)."
[2:253] Those messengers We endowed with gifts, some above others: To one of them Allah spoke; others He raised to degrees (of honour); to Jesus the son of Mary We gave clear (Signs), and strengthened him with the holy spirit. If Allah had so willed, succeeding generations would not have fought among each other, after clear (Signs) had come to them, but they (chose) to wrangle, some believing and others rejecting. If Allah had so willed, they would not have fought each other; but Allah Fulfilleth His plan.
[3:45] Behold! the angels said: "O Mary! Allah giveth thee glad tidings of a Word from Him: his name will be Christ Jesus, the son of Mary, held in honour in this world and the Hereafter and of (the company of) those nearest to Allah;
[3:52] When Jesus found Unbelief on their part He said: "Who will be My helpers to (the work of) Allah?" Said the disciples: "We are Allah's helpers: We believe in Allah, and do thou bear witness that we are Muslims.
[3:55] Behold! Allah said: "O Jesus! I will take thee and raise thee to Myself and clear thee (of the falsehoods) of those who blaspheme; I will make those who follow thee superior to those who reject faith, to the Day of Resurrection: Then shall ye all return unto me, and I will judge between you of the matters wherein ye dispute.
[3:59] The similitude of Jesus before Allah is as that of Adam; He created him from dust, then said to him: "Be". And he was.
[3:84] Say: "We believe in Allah, and in what has been revealed to us and what was revealed to Abraham, Isma'il, Isaac, Jacob, and the Tribes, and in (the Books) given to Moses, Jesus, and the prophets, from their Lord: We make no distinction between one and another among them, and to Allah do we bow our will (in Islam)."
[4:157] That they said (in boast), "We killed Christ Jesus the son of Mary, the Messenger of Allah";- but they killed him not, nor crucified him, but so it was made to appear to them, and those who differ therein are full of doubts, with no (certain) knowledge, but only conjecture to follow, for of a surety they killed him not:-
[4:163] We have sent thee inspiration, as We sent it to Noah and the Messengers after him: we sent inspiration to Abraham, Isma'il, Isaac, Jacob and the Tribes, to Jesus, Job, Jonah, Aaron, and Solomon, and to David We gave the Psalms.
[4:171] O People of the Book! Commit no excesses in your religion: Nor say of Allah aught but the truth. Christ Jesus the son of Mary was (no more than) a messenger of Allah, and His Word, which He bestowed on Mary, and a spirit proceeding from Him: so believe in Allah and His messengers. Say not "Trinity" : desist: it will be better for you: for Allah is one Allah: Glory be to Him: (far exalted is He) above having a son. To Him belong all things in the heavens and on earth. And enough is Allah as a Disposer of affairs.
[5:46] And in their footsteps We sent Jesus the son of Mary, confirming the Law that had come before him: We sent him the Gospel: therein was guidance and light, and confirmation of the Law that had come before him: a guidance and an admonition to those who fear Allah.
[5:78] Curses were pronounced on those among the Children of Israel who rejected Faith, by the tongue of David and of Jesus the son of Mary: because they disobeyed and persisted in excesses.
[5:110] Then will Allah say: "O Jesus the son of Mary! Recount My favour to thee and to thy mother. Behold! I strengthened thee with the holy spirit, so that thou didst speak to the people in childhood and in maturity. Behold! I taught thee the Book and Wisdom, the Law and the Gospel and behold! thou makest out of clay, as it were, the figure of a bird, by My leave, and thou breathest into it and it becometh a bird by My leave, and thou healest those born blind, and the lepers, by My leave. And behold! thou bringest forth the dead by My leave. And behold! I did restrain the Children of Israel from (violence to) thee when thou didst show them the clear Signs, and the unbelievers among them said: 'This is nothing but evident magic.'
[5:112] Behold! the disciples, said: "O Jesus the son of Mary! can thy Lord send down to us a table set (with viands) from heaven?" Said Jesus: "Fear Allah, if ye have faith."
[5:114] Said Jesus the son of Mary: "O Allah our Lord! Send us from heaven a table set (with viands), that there may be for us - for the first and the last of us - a solemn festival and a sign from thee; and provide for our sustenance, for thou art the best Sustainer (of our needs)."
[5:116] And behold! Allah will say: "O Jesus the son of Mary! Didst thou say unto men, worship me and my mother as gods in derogation of Allah'?" He will say: "Glory to Thee! never could I say what I had no right (to say). Had I said such a thing, thou wouldst indeed have known it. Thou knowest what is in my heart, Thou I know not what is in Thine. For Thou knowest in full all that is hidden.
[6:85] And Zakariya and John, and Jesus and Elias: all in the ranks of the righteous:
[19:34] Such (was) Jesus the son of Mary: (it is) a statement of truth, about which they (vainly) dispute.
[33:7] And remember We took from the prophets their covenant: As (We did) from thee: from Noah, Abraham, Moses, and Jesus the son of Mary: We took from them a solemn covenant:
[42:13] The same religion has He established for you as that which He enjoined on Noah - the which We have sent by inspiration to thee - and that which We enjoined on Abraham, Moses, and Jesus: Namely, that ye should remain steadfast in religion, and make no divisions therein: to those who worship other things than Allah, hard is the (way) to which thou callest them. Allah chooses to Himself those whom He pleases, and guides to Himself those who turn (to Him).
[43:57] When (Jesus) the son of Mary is held up as an example, behold, thy people raise a clamour thereat (in ridicule)!
[43:61] And (Jesus) shall be a Sign (for the coming of) the Hour (of Judgment): therefore have no doubt about the (Hour), but follow ye Me: this is a Straight Way.
[43:63] When Jesus came with Clear Signs, he said: "Now have I come to you with Wisdom, and in order to make clear to you some of the (points) on which ye dispute: therefore fear Allah and obey me.
[57:27] Then, in their wake, We followed them up with (others of) Our messengers: We sent after them Jesus the son of Mary, and bestowed on him the Gospel; and We ordained in the hearts of those who followed him Compassion and Mercy. But the Monasticism which they invented for themselves, We did not prescribe for them: (We commanded) only the seeking for the Good Pleasure of Allah; but that they did not foster as they should have done. Yet We bestowed, on those among them who believed, their (due) reward, but many of them are rebellious transgressors.
[61:6] And remember, Jesus, the son of Mary, said: "O Children of Israel! I am the messenger of Allah (sent) to you, confirming the Law (which came) before me, and giving Glad Tidings of a Messenger to come after me, whose name shall be Ahmad." But when he came to them with Clear Signs, they said, "this is evident sorcery!"
[61:14] O ye who believe! Be ye helpers of Allah: As said Jesus the son of Mary to the Disciples, "Who will be my helpers to (the work of) Allah?" Said the disciples, "We are Allah's helpers!" then a portion of the Children of Israel believed, and a portion disbelieved: But We gave power to those who believed, against their enemies, and they became the ones that prevailed. In the Arabic original text of the holy Quran, Jesus Peace be upon Him is mentioned explicitly by name exactly 25 times.
Three verses of the Noble verses mentioned above don't have His explicit name but it's mentioned in the translation for clarification.