The Quran talks about "beautiful names of Allah" and the hadiths further specify that there is exactly 99 names. Muslims are supposed to learn these these names of Allah, but there is a problem, because Muhammad didn't offer the full list of these names. Islamic scholars had to rely on ijtihad to find these names in the Quran and sunnah and different scholars came up with different lists. Out of the supposed 99 names of Allah, they together found at least 276 names.
Some apologetic sources (including Wikipedia) claim that according to the hadith, there are at least 99 names. But the hadith doesn't say "at least". It says simply ninety-nine (تِسْعَةً وَتِسْعِينَ) and even adds that it's one hundred minus one, which seems to emphasize, that it is exactly 99 and not 100 or more. And the hadith also says that who memorizes all these names would go to paradise - such a task would be hard in the time of Muhammad, considering that in that time the ummah was illiterate. And even today, as we'll see, it seems impossible to find the 99 names.
The most popular list of 99 names of Allah among Muslims (which is also used on Wikipedia) seems to be a list from a weak (da'if) hadith from the collection of Tirmidhi.
Abu Hurairah narrated that the Messenger of Allah (ﷺ) said:
“Indeed, Allah has ninety-nine Names, one hundred less one, whoever counts them shall enter Paradise. He is Allah, the one whom there is none worthy of worship except for Him (Allāhu Lā Ilāha Illā Huwa), the Most Merciful (to the creation) (Ar-Raḥmān), the Most Beneficent (to the believers) (Ar-Raḥīm), the King (Al-Malik), the Free of Deficiencies (Al-Quddūs), the Granter of Safety (As-Salām), the Granter of Security (Al-Mu’min), the Watcher (Al-Muhaimin), the Mighty (Al-`Azīz), the Compeller (Al-Jabbār), the Supreme (Al-Mutakabbir), the Creator (Al-Khāliq), the Originator (Al-Bāri’), the Fashioner (Al-Muṣawwir), the Pardoner (Al-Ghaffār), the Overwhelming (Al-Qahhār), the Giving (Al-Wahhāb), the Provider (Ar-Razzāq), the Opener (Al-Fattāḥ), the Knowing (Al-`Alīm), the Taker (Al-Qābiḍ), the Giver (Al-Bāsiṭ), the Abaser (Al-Khāfiḍ), the Exalter (Ar-Rāfi`), the One who grants honor (Al-Mu`izz), the One who humiliates (Al-Mudhil), the Hearing (As-Samī`), the Seeing (Al-Baṣīr), the Judge (Al-Ḥakam), the Just (Al-`Adl), the Kind (Al-Laṭīf), the Aware (Al-Khabīr), the Forbearing (Al-Ḥalīm), the Magnificent (Al-`Aẓīm), the Oft-Forgiving (Al-Ghafūr), the Grateful (Ash-Shakūr), the Most High (Al-`Aliyy), the Great (Al-Kabīr), the Guardian (Al-Ḥafīẓ), the Powerful (Al-Muqīt), the Reckoner (Al-Ḥasīb), the Glorious (Al-Jalīl), the Generous (Al-Karīm), the Watcher (Ar-Raqīb), the Responder (Al-Mujīb), the Liberal Giver (Al-Wāsi`), the Wise (Al-Ḥakīm), the Loving (Al-Wadūd), the Majestic (Al-Majīd), the Reviver (Al-Bā`ith), the Witness (Ash-Shahīd), the Truth (Al-Ḥaqq), the Guarantor (Al-Wakīl), the Strong (Al-Qawiyy), the Firm (Al-Matīn), the One Who Aids (Al-Waliyy), the Praiseworthy (Al-Ḥamīd), the Encompasser (Al-Muḥṣi), the One Who Begins things (Al-Mubdi’), the One Who brings things back (Al-Mu`īd), the One Who gives life (Al-Muḥyi), the One Who causes death (Al-Mumīt), the Living (Al-Ḥayyu), the Self-Sufficient (Al-Qayyūm), the One Who brings into existence (Al-Wājid), the Illustrious (Al-Mājid), the One (Al-Wāḥid), the Master (Aṣ-Ṣamad), the Able (Al-Qādir), the Powerful (Al-Muqtadir), the One who hastens (Al-Muqaddim), the One who delays (Al-Mu’akhkhir), the First (Al-Awwal), the Last (Al-Ākhir), the Apparent (Aẓ-Ẓāhir), the Inner (Al-Bāṭin), the Owner (Al-Wāli), the Exalted (Al-Muta`āli), the Doer of Good (Al-Barr), the Acceptor of repentance (At-Tawwāb), the Avenger (Al-Muntaqim), the Pardoning (Al-`Afuww), the Kind (Ar-Ra’ūf), the Owner of Dominion (Mālikul-Mulk), the Possessor of Glory and Generosity (Dhul Jalāli wal Ikrām), the One who does justice (Al-Muqsiṭ), the Gatherer (Al-Jāmi`), the Rich (Al-Ghaniyy), the Enricher (Al-Mughni), the Preventer (Al-Māni`), the Harmer (Aḍ-Ḍār), the One who benefits (An-Nāfi`), the Light (An-Nūr), the Guide (Al-Hādi), the Originator (Al-Badī`), the Lasting (Al-Bāqi), the Inheritor (Al-Wārith), the Guide (Ar-Rashīd), the Tolerant (Aṣ-Ṣabūr).”