How Many Names of Allah?

Those are two
The first one is from the Quran

((اللَّهُ ، الرَّحْمَنُ ، الرَّحِيمُ ، الْمَلِكُ ، الْقُدُّوسُ ، السَّلامُ ، الْمُؤْمِنُ ، الْمُهَيْمِنُ ، الْعَزِيزُ ، الْجَبَّارُ ، الْمُتَكَبِّرُ ، الْخَالِقُ ، الْبَارِئُ ، الْمُصَوِّرُ ، الْغَفَّارُ ، الْقَهَّارُ ، التَّوَّابُ ، الْوَهَّابُ ، الخلاّقُ ، الرَّزَّاقُ ، الْفَتَّاحُ ، الْعَلِيمُ ، الْحَلِيمُ ، الْعَظِيمُ ، الْوَاسِعُ ، الْحَكِيمُ ، الْحَيُّ ، الْقَيُّومُ ، السَّمِيعُ ، الْبَصِيرُ ، اللَّطِيفُ ، الْخَبِيرُ ، الْعَلِيُّ ، الْكَبِيرُ ، المحيطُ ، القديرُ ، المولى ، النّصيرُ ، الْكَرِيمُ ، الرَّقِيبُ ، القريبُ ، الْمُجِيبُ ، الْوَكِيلُ ، الْحَسِيبُ ، الْحَفِيظُ ، الْمُقِيتُ ، الْوَدُودُ ، الْمَجِيدُ ، الْوَارِثُ ، الشَّهِيدُ ، الْوَلِيُّ ، الْحَمِيدُ ، الْحَقُّ ، المبينُ ، الْقَوِيُّ ، الْمَتِينُ ، الْغَنِيُّ ، المالكُ ، الشّديدُ ، الْقَادِرُ ، الْمُقْتَدِرُ ، القاهرُ ، الكافي ، الشّاكرُ ، المستعانُ ، الفاطرُ ، الْبَدِيعُ ، الغافرُ ، الأَوَّلُ ، الآخِرُ ، الظَّاهِرُ ، الْبَاطِنُ ، الكفيلُ ، الغالبُ ، الْحَكَمُ ، العالِمُ ، الرّفيعُ ، الحافظُ ، الْمُنْتَقِمُ ، القائمُ ، الْمُحْيِي ، الْجَامِعُ ، المليكُ ، الْمُتَعَالِي ، النُّورُ ، الْهَادِي ، الْغَفُورُ ، الشَّكُورُ ، الْعَفُوُّ ، الرَّءُوفُ ، الأكرمُ ، الأعلى ، الْبَرُّ ، الحفيُّ ، الربُّ ، الإلهُ ، الْوَاحِدُ ، الأحدُ ، الصَّمَدُ الَّذي لَمْ يَلِدْ وَلَمْ يُولَدْ وَلَمْ يَكُنْ لَهُ كُفُوًا أَحَدٌ)]) .

And those from the Quran and sunnah

اللَّهُ ، الأحدُ ، الأعلى ، الأكرم ، الإله ، الأَوَّلُ ، الآخِرُ ، الظَّاهِرُ ، الْبَاطِنُ ، الْبَارِئُ ، الْبَرُّ ، الْبَصِيرُ ، التَّوَّابُ ، الْجَبَّارُ ، الحافظُ ، الْحَسِيبُ ، الْحَفِيظُ ، الحفيُّ ، الْحَقُّ ، المبينُ ، الْحَكِيمُ ، الْحَلِيمُ ، الْحَمِيدُ ، الْحَيُّ ، الْقَيُّومُ ، الْخَبِيرُ ، الْخَالِقُ ، الخلاّقُ ، الرّؤوفُ ، الرَّحْمَنُ ، الرَّحِيمُ ، الرَّزَّاقُ ، الرَّقِيبُ ، السَّلامُ ، السَّمِيعُ ، الشّاكرُ ، الشَّكُورُ ، الشَّهِيدُ ، الصَّمَدُ ، العالمُ ، الْعَزِيزُ ، الْعَظِيمُ ، الْعَفُوُّ ، الْعَلِيمُ ، الْعَلِيُّ ، الْغَفَّارُ ، الْغَفُورُ ، الْغَنِيُّ ، الْفَتَّاحُ ، الْقَادِرُ ، القاهر ، الْقُدُّوسُ ، القدير ، القريب ، الْقَوِيُّ ، الْقَهَّارُ ، الْكَبِيرُ ، الْكَرِيمُ ، اللَّطِيفُ ، الْمُؤْمِنُ ، الْمُتَعَالِي ، الْمُتَكَبِّرُ ، الْمَتِينُ ، الْمُجِيبُ ، الْمَجِيدُ ، المحيط ، الْمُصَوِّرُ ، الْمُقْتَدِرُ ، الْمُقِيتُ ، الْمَلِكُ ، المليك ، المولى ، الْمُهَيْمِنُ ، النّصير ، الْوَاحِدُ ، الْوَارِثُ ، الْوَاسِعُ ، الْوَدُودُ ، الْوَكِيلُ ، الْوَلِيُّ ، الْوَهَّابُ ]) .
: ((الجميل ، الجواد ، الْحَكَمُ ، الحيي ، الربّ ، الرّفيق ، السبوّح ، السيّد ، الشّافي ، الطيّب ، الْقَابِضُ ، الْبَاسِطُ ، الْمُقَدِّمُ ، الْمُؤَخِّرُ ، المحسن ، المعطي ، المنّان ، الوتر)) .
The first one by counting of ibnu hadjar and the second one is by ibnu uthaymin
I hope that help you

There are more that 100 because in this hadith we say :
I call upon you by every one of the beautiful names with which you have described yourself, or which you have revealed in your Book, or you have taught to anyone of your creatures, or which you have chosen to keep in the knowledge of the unseen with you,

Ibn Mas’ud reported: The Messenger of Allah, peace and blessings be upon him, said, “If any Muslim is afflicted with distress and makes this supplication, then his supplication will be answered: O Allah, I am your servant, the son of your servant, the son of your maidservant. My forelock is in your hand, your command concerning me prevails, and your decision concerning me is just. I call upon you by every one of the beautiful names with which you have described yourself, or which you have revealed in your Book, or you have taught to anyone of your creatures, or which you have chosen to keep in the knowledge of the unseen with you, to make the Quran the delight of my heart, the light of my chest, and to remove my sadness and dispel my anxiety.” The Prophet said, “If he says this, Allah will remove his affliction and replace it with joy and happiness.” They said, “O Messenger of Allah, should we not learn it?” The Prophet said, “Yes, whoever hears it should know it.”

Jazak'Allah khair for your answers, sister!

You are welcome sister.

assalamualekum

There is a list of supposed names of Allah in the Haidth, but this list is inauthentic and hence should not be listened to. The scholars who reject this list (in the hadith) as inauthentic are, at-Tirmidhi, al-Baihaqi, ibn Hazm, al-Dawudi, ibn Taymiya, ibn Katheer, ibn Hajr, al-Juwaini, ibn Baz, al-Albani, ibn Uthaimin and Abdul Qadir al-Arnaut.

لِلَّهِ تِسْعَةٌ وَتِسْعُونَ اسْمًا، مِائَةٌ إِلاَّ وَاحِدًا، لاَ يَحْفَظُهَا أَحَدٌ إِلاَّ دَخَلَ الْجَنَّةَ، وَهْوَ وَتْرٌ يُحِبُّ الْوَتْرَAllah has ninety-nine Names, one hundred minus one, and whoever believes in their meanings and acts accordingly, will enter Paradise; and Allah is witr (one) and loves 'the witr'
bukhari shareef

There are ninety-nine names mentioned in the Quran, and in authentic Ahadith, anything other than these names are weak or fabricated.
Allah know better

infinite

There are 99 names of Allah mentioned in the Quran.

And to Allah belong the best names, so invoke Him by them - Surat Al-A’raf 7:180


Allah – there is no deity except Him. To Him belong the best names. - Surat Taha 20:8


Narrated Abu Huraira: Prophet Muhammad SAW said, “Allah has ninety-nine names, i.e. one-hundred minus one, and whoever knows them will go to Paradise.”

Sahih Al-Bukhari – Book 50 Hadith 894

Abu Huraira reported Prophet Muhammad SAW as saying: Verily, there are ninety-nine names for Allah, i.e. hundred excepting one. He who enumerates them would get into Paradise. And Hammam has made this addition on the authority of Abu Huraira who reported it from Prophet Muhammad SAW that he said: “He is Odd (one) and loves odd number.”

Sahih Muslim – Book 35 Hadith 6476


99 names - http://www.searchtruth.com/Allah/99Names.php


Dr. Philip and other modern western islamic speakers are not that strong in their knowledge, they did not spend a life time of studying from a young age. It's ok if you want to listen to them, but they should not be the sole source of learning one's deen.