What are the names of the gates of Heaven?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
If your question is about the gates of heaven, i.e., the firmament, there is no evidence proving their exact number. Allah Says (interpretation of meaning): {Verily, those who belie Our Ayât (proofs, evidences, verses, lessons, signs, revelations, etc.) and treat them with arrogance, for them the gates of heaven will not be opened,}[7:40].
One can deduce from this that the firmament has several gates. The Prophet said in the sound Hadith of Isra and Miraj: "…When I reached the nearest heaven. Gabriel said to the heaven gate-keeper, 'Open the gate.' The gatekeeper asked, 'Who is it?' He said, 'Gabriel.' The gate-keeper asked, 'Who is accompanying you?' Gabriel said, 'Muhammad.' The gate-keeper said, 'Has he been called?' Gabriel said, 'Yes.' Then it was said, 'He is welcomed…"
The same question was asked on every gate of heaven.

So this is yet another evidence that every heaven has a gate or several gates.
If your question is about the gates of paradise, there are many concordant Hadith from the Prophet stating that The Paradise has eight gates. There are other Hadith which do not specify a given number to the gates of Paradise.
Al Bukhari and Muslim reported from Sahl Ibn Saad that he narrated that the Prophet said: "The Paradise has eight gates. One of them (these gates) is called Al Rayyan, only the fasting people (people who used to perform fasting during their lives) can come through it".
Muslim narrated from Ubadata Ibn Al Samit that the Prophet said: Allah's Apostle said, "Whoever gives two kinds (of things or property) in charity for Allah's cause, will be called from the gates of Paradise and will be addressed, 'O slaves of Allah! Here is prosperity.' So, whoever was amongst the people who used to offer their prayers, will be called from the gate of the prayer; and whoever was amongst the people who used to participate in Jihad, will be called from the gate of Jihad; and whoever was amongst those who used to observe fasts, will be called from the gate of Ar-Rayyan; whoever was amongst those who used to give in charity, will be called from the gate of charity." Abu Bakr said, "Let my parents be sacrificed for you, O Allah's Apostle! No distress or need will befall him who will be called from those gates. Will there be any one who will be called from all these gates?" The Prophet replied, "Yes, and I hope you will be one of them."
[Reported by Imam Al Bukhari and Imam Muslim].
Ibn Abi Hatim narrated from Ibn Abbas that he said: "Paradise has eight gates: a gate for the praying, a gate for the fasting, a gate for those who perform Hajj, a gate for those who perform Umrah, a gate for Mujahideen (those who fight for the sake of Allah) a gate for Al Dhakireen (those remember Allah and supplicate Him) and a gate for Al Shakireen (those who thank Allah)". Reported by Al Suyuty in his book: Al Dur Al Manthoor.
It is also narrated in some Ahadith that there is a gate in Paradise for each kind of good deed.
Ahmad and Ibn Abi Shaibah reported in a Hadith narrated from Abu Huraira that he said that the Prophet said: "Each group of people is called to enter Paradise by a door named after the kind of good deeds they used to perform".
We conclude this Fatwa with what Al Munawi said about the gates of Paradise. He said: "The gates of Paradise are eight because the key to Paradise is La Ilaha Illa llah (None deserves to be worshipped except Allah) and this key has eight bits: (1) prayer (2) fasting (3) Zakah (4) Hajj (5) Jihad (6) enjoining the right (7) forbidding the evil and bad (8) beneficence and tightening of kinship relations.
So, since the kinds of good deeds are eight the gates of paradise are also eight. May Allah have Mercy on us all.
Allah knows best.