Short answer
His name is Muhammad ibn Abdullah ibn Abd al-Muttalib ibn Hashim, of Quraysh, and his kunya was Abu al-Qasim. He said he had several names: Muhammad, Ahmad, al-Mahi, al-Hashir and al-Aqib. The Quran also calls him the Messenger of Allah, the Prophet, and a mercy to the worlds.
Sunni scholars agree on his lineage up to Adnan, a descendant of Ismail. His names in the Quran and authentic hadith include Muhammad, Ahmad, al-Mahi, al-Hashir and al-Aqib; many other descriptions are titles rather than proper names.
The four schools agree on this.
Explanation
Full name and lineage. He is Muhammad, son of Abdullah, son of Abd al-Muttalib (whose name was Shayba), son of Hashim, son of Abd Manaf, son of Qusayy, son of Kilab, and so on up to Adnan, a descendant of the prophet Ismail son of Ibrahim. Scholars agree on the line up to Adnan and are cautious about the names above him. His mother was Aminah bint Wahb, of Banu Zuhra. His kunya (name as father) was Abu al-Qasim, after his first son. See the family tree.
His names. He said: "I have names: I am Muhammad, I am Ahmad, I am al-Mahi through whom Allah wipes out disbelief, I am al-Hashir at whose feet people will be gathered, and I am al-Aqib," meaning the last, after whom there is no prophet. Muhammad means "the much praised" and Ahmad "the most praising" or "most praised". The Quran uses both: Muhammad in 48:29 and other verses, and Ahmad in Isa's good news (61:6).
Titles. Before prophethood Quraysh called him al-Amin, the trustworthy. The Quran calls him Rasul Allah (the Messenger of Allah), al-Nabi (the Prophet), the seal of the prophets, a mercy to the worlds, a bringer of good news and a warner. Scholars have written books listing hundreds of such descriptions.
When Muslims mention him they add "sallallahu alayhi wa sallam" (ﷺ), may Allah bless him and grant him peace. On naming children Muhammad, see Is it sunnah to name your child Muhammad?; on the meaning of the name, see Muhammad name meaning.
The evidence
Quran, Surah Al-Fath 48:29
مُّحَمَّدٌۭ رَّسُولُ ٱللَّهِ ۚ وَٱلَّذِينَ مَعَهُۥٓ أَشِدَّآءُ عَلَى ٱلْكُفَّارِ رُحَمَآءُ بَيْنَهُمْ ۖ تَرَىٰهُمْ رُكَّعًۭا سُجَّدًۭا يَبْتَغُونَ فَضْلًۭا مِّنَ ٱللَّهِ وَرِضْوَٰنًۭا ۖ سِيمَاهُمْ فِى وُجُوهِهِم مِّنْ أَثَرِ ٱلسُّجُودِ ۚ ذَٰلِكَ مَثَلُهُمْ فِى ٱلتَّوْرَىٰةِ ۚ وَمَثَلُهُمْ فِى ٱلْإِنجِيلِ كَزَرْعٍ أَخْرَجَ شَطْـَٔهُۥ فَـَٔازَرَهُۥ فَٱسْتَغْلَظَ فَٱسْتَوَىٰ عَلَىٰ سُوقِهِۦ يُعْجِبُ ٱلزُّرَّاعَ لِيَغِيظَ بِهِمُ ٱلْكُفَّارَ ۗ وَعَدَ ٱللَّهُ ٱلَّذِينَ ءَامَنُوا۟ وَعَمِلُوا۟ ٱلصَّٰلِحَٰتِ مِنْهُم مَّغْفِرَةًۭ وَأَجْرًا عَظِيمًۢا ﴿٢٩﴾
Muhammad is the Messenger of Allah; and those with him are forceful against the disbelievers, merciful among themselves. You see them bowing and prostrating [in prayer], seeking bounty from Allah and [His] pleasure. Their mark is on their faces from the trace of prostration. That is their description in the Torah. And their description in the Gospel is as a plant which produces its offshoots and strengthens them so they grow firm and stand upon their stalks, delighting the sowers - so that Allah may enrage by them the disbelievers. Allah has promised those who believe and do righteous deeds among them forgiveness and a great reward.
The name Muhammad in the Quran.
Quran, Surah As-Saff 61:6
وَإِذْ قَالَ عِيسَى ٱبْنُ مَرْيَمَ يَٰبَنِىٓ إِسْرَٰٓءِيلَ إِنِّى رَسُولُ ٱللَّهِ إِلَيْكُم مُّصَدِّقًۭا لِّمَا بَيْنَ يَدَىَّ مِنَ ٱلتَّوْرَىٰةِ وَمُبَشِّرًۢا بِرَسُولٍۢ يَأْتِى مِنۢ بَعْدِى ٱسْمُهُۥٓ أَحْمَدُ ۖ فَلَمَّا جَآءَهُم بِٱلْبَيِّنَٰتِ قَالُوا۟ هَٰذَا سِحْرٌۭ مُّبِينٌۭ ﴿٦﴾
And [mention] when Jesus, the son of Mary, said, "O children of Israel, indeed I am the messenger of Allah to you confirming what came before me of the Torah and bringing good tidings of a messenger to come after me, whose name is Ahmad." But when he came to them with clear evidences, they said, "This is obvious magic."
The name Ahmad in the Quran.
Quran, Surah Al-Anbiyaa 21:107
وَمَآ أَرْسَلْنَٰكَ إِلَّا رَحْمَةًۭ لِّلْعَٰلَمِينَ ﴿١٠٧﴾
And We have not sent you, [O Muhammad], except as a mercy to the worlds.
One of his Quranic titles.
Sahih al-Bukhari 4896
Sahih... أنا محمد وأنا أحمد وأنا الماحي ...
"I am Muhammad, I am Ahmad, and I am al-Mahi."
His own list of his names.
Where the ruling is recorded
- al-Shama'il al-Muhammadiyya (al-Tirmidhi), Chapter on the names of the Messenger of Allah. The hadith of his names.
- Zad al-Ma'ad (Ibn al-Qayyim), Opening section on his lineage and his names. His lineage to Adnan and the meaning of each name.
- Sirat Ibn Hisham, Opening chapter on the lineage of the Messenger of Allah. His line from Adnan to Ismail and Ibrahim.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.