Praise be to Allah.
Soorat al-Isra’ is called Soorat Bani Israa’eel in two saheeh mawqoof hadeeths, in which it is the words of the Sahaabah (may Allah be pleased with them):
The first hadeeth was narrated from ‘Abd-Allah ibn Mas‘ood (may Allah be pleased with him), who said concerning (the soorahs) Bani Israa’eel, al-Kahf, Maryam, Ta-Ha and al-Anbiya’: They are among the best and earliest and they are among the first I received.
Narrated by al-Bukhaari, 4994
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: ‘Itaaq (translated above as “best”) is the plural of ‘ateeq, which means ancient, or it may mean everything that reaches the utmost of excellence; the second meaning was preferred by a number of scholars in this hadeeth.
“and they are among the first I received (tilaadi)” i.e., among that which I memorized a long time ago. Tilaad means long-standing possession; it is the opposite of taarif (recent acquisition). What Ibn Mas‘ood meant was that they were among the first soorahs he learned of the Qur’aan, and that they possess virtue because of what they contain of stories of the earlier Prophets and nations.
End quote from Fath al-Baari, 8/388
The second hadeeth was narrated from ‘Aa’ishah (may Allah be pleased with her) who said: The Prophet (blessings and peace of Allah be upon him) used not to sleep until he had recited Bani Israa’eel and al-Zumar. Narrated by al-Tirmidhi, 3402, who said: It is a hasan hadeeth. It was also classed as hasan by al-Haafiz Ibn Hajar in Nataa’ij al-Afkaar, 3/65; and it was classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
The scholars said that this soorah was better known by the name Soorat Bani Isra’eel at the time of the Sahaabah and Taabi’een, because the first verse of Soorat al-Isra’ speaks of the Isra’ (Night Journey) to al-Masjid al-Aqsa, then in the second verse it starts to speak of an important stage in the story of Bani Isra’eel (the Children of Israel) and their mischief in the land, which is not mentioned in any of the stories of Bani Isra’eel anywhere else in the Qur’aan. That is in the passage where Allah, may He be exalted, says (interpretation of the meaning):
“Glorified (and Exalted) is He (Allâh) [above all that (evil) they associate with Him]. Who took His slave (Muhammad (blessings and peace of Allah be upon him)) for a journey by night from Al-Masjid-al-Harâm (at Makkah) to Al-Masjid-al-Aqsa (in Jerusalem), the neighbourhood whereof We have blessed, in order that We might show him (Muhammad (blessings and peace of Allah be upon him)) of Our Ayât (proofs, evidences, lessons, signs, etc.). Verily, He is the All-Hearer, the All-Seer
2. And We gave Mûsa (Moses) the Scripture and made it a guidance for the Children of Israel (saying): ‘Take not other than Me as (your) Wakîl (Protector, Lord, or Disposer of your affairs).
3. ‘O offspring of those whom We carried (in the ship) with Nûh (Noah)! Verily, he was a grateful slave.’
4. And We decreed for the Children of Israel in the Scripture, indeed you would do mischief in land twice and you will become tyrants and extremely arrogant!”
Al-‘Allaamah al-Taahir ibn ‘Ashoor (may Allah have mercy on him) said:
In many Mushafs it is called Soorat al-Isra’. Al-Aloosi stated that it is called by this name, because at the beginning it mentions the Isra’ (Night Journey) of the Prophet (blessings and peace of Allah be upon him) and that is the only place where it is mentioned. But at the time of the Sahaabah it was called Soorat Bani Israa’eel, the reason for that being that it mentions things about Bani Isra’eel that are not mentioned in other soorahs, namely their subjugation by those who were given to terrible warfare (cf. 17:4) -- the Assyrians; then their subjugation by another people -- namely the Romans. It is also called Soorat Subhaan, because it begins with this word.
End quote from al-Tahreer wal-Tanweer, 15/5
See also the answer to question no. 131664
And Allah knows best.