How many Prophets' name is in the Holy Qur'an? Who all are they?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Allah has mentioned 25 names of Messengers and Prophets in the Qur'an. In Surah Al-An'am [6: 83-86], Allah mentioned 18 names and the remaining ones are mentioned in other different Surah, they are: Adam , H'ud , Saleh , Shuaib , Ismael , Idriss , Dhu Al-Kifl and Prophet Muhammad (Sallallahu Alaihi wa Sallam). Allah Says (interpretation of meaning): {Allâh chose Adam, Nûh (Noah), …} [3: 33]. Allah also Says (interpretation of meaning): {And to 'Ad (people We sent) their brother Hûd. …} [11: 50]. He also Says: {And to Thamûd (people, We sent) their brother Sâlih (Saleh). …} [11: 61]. Allah Says (interpretation of meaning): {And to the Madyan (Midian) people (We sent) their brother Shu'aib. …} [11: 84]. He Says: {And (remember) Isma'îl (Ishmael), and Idris (Enoch) and Dhul-Kifl (Isaiah), …} [21: 85].
As for the 18 that were mentioned in Al An'am they are as Allah Says (interpretation of meaning): {And that was Our Proof which We gave Ibrâhim (Abraham) against his people. We raise whom We will in degrees. Certainly your Lord is All-Wise, All-Knowing. And We bestowed upon him Ishâque (Isaac) and Ya'qûb (Jacob), each of them We guided, and before him, We guided Nûh (Noah), and among his progeny Dawûd (David), Sulaimân (Solomon), Ayub (Job), Yûsuf (Joseph), Mûsa (Moses), and Hârûn (Aaron). Thus do We reward the gooddoers. And Zakariyâ (Zachariya), and Yahya (John) and 'Iesa (Jesus) and Iliyâs (Elias), each one of them was of the righteous. And Ismâ'il (Ishmael) and Al-Yas'â (Elisha), and Yûnus (Jonah) and Lout (Lot), and each one of them We preferred above the 'Alamîn (mankind and jinns) (of their times).} [6: 83-86].
Four of these were Arabs: " H'ud , Saleh , Shu'aib and Muhammad ".
The Sunnah mentioned some Prophets' names that were not mentioned in the Qur'an. First, there is Shitha . Ibn Katheer said: 'He was a Prophet, this is reported by Ibn Hibban from Abu Dharr that 50 pamphlets were revealed to Shitha .
Second, there is Yusha' Ibn Noun . Muslim reported from Abu Hurairah that he said: "One of the Prophets was in a war … then he said to the Sun 'you are ordered as I am ordered, O Allah! Stop it for a while for me" .
What proves that this Prophet is Yusha' Ibn Noun , Musa 's servant is the Hadith reported by Ahmad that the sun was never withheld except for Yusha' during his night trip to Jerusalem.
There is a disagreement among scholars regarding three people that were mentioned in the Qur'an whether they are Prophets or not. These people are Dhul Qarnain , Tubb'a and Al-Khadir . Some scholars believe that all of them are Prophets. But this is difficult to prove since it reported in a sound Hadith that the Prophet (Sallallahu Alaihi wa Sallam) said: "I do not know whether Tubb'aa was a Prophet. Neither do I know whether Dhul Qarnain was a Prophet or not" .
As for Al-Khadir the most preponderant opinion is that he was a Prophet as Allah Says (interpretation of meaning) at the end of his story: {… And I did it not of my own accord. …} [18: 82]. This implies that the acts he did were revealed to him.
Allah knows best.