Question Summary:
Why are the names of the same prophets different in both the Bible and Holy Qur’an?

Question Detail:

Asalamualaiykkum,
                      Why the names of same prophets are different in both Bible and Holy Quran?

Answer :

Answer:
In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
The names of many Prophets (Anbiya) (Alayhim al-Salaam) have been mentioned in the Bible as well as in the Holy Qur’an. Many Anbiyaa (Alayhim al-Salaam) were of different cultural, social and linguistic backgrounds. For example, Hadhrat Ismail (Alayhi al-Salaam) spoke the Hebrew language.
Since the Qur’an is in Arabic language, the names of such Anbiyaa (Alayhim al-Salaam) were Arabasized from Hebrew, etc. in order to accommodate for the Arabic phonetic, linguistics, etc.
This does not mean that the actual name has changed. Rather, it is a variant version of the name in another language.
For example:
1. Ismail (Alahi al-Salaam) was Ishmael (Hebrew: יִשְׁמָעֵאל , Modern Yishma'el Tiberian Yišmāʻēl ISO 259-3 Yišmaˁel; Greek: Ισμαήλ Ismaēl; Latin: Ismael; Arabic: إسماعيل‎ ʾIsmāʿīl) is a figure in the Hebrew Bible and the Qur'an, and was Abraham's first son according to Jews, Christians and Muslims[1]
2. Ya’qub (Alayhi al-Salaam) was from the Latin Iacobus, which was from the Greek Ιακωβος (Iakobos), which was from the Hebrew name יַעֲקֹב (Ya'aqov). The English names Jacob and James derive from the same source, with James coming from Latin Iacomus, a later variant of Iacobus. Unlike English, many languages do not have separate spellings for the two names. [2]
And Allah Ta’āla Knows Best 
Moulana Ismail Desai,
Student Darul Iftaa
Durban, South Africa
Checked and Approved by,
Mufti Ebrahim Desai.