As an addition to the Answer of @مجاهد :
- In (tafsir) at-tahrir wa-tanwir i found another name (My own translation, so be careful):
اليسع: the hebrew original name is Elysha' and he was changed into al-Yas'a in Arabic.
He is the son of Shafit
شافاط from the people of Eel Maholah آبل محولة. He was a farmer before he became a Prophet taught by the Prophet Elias إلياس (May peace be upon him) (who according a narration of ibn 'Abbas (peace be upon both of them) was his uncle) during the reign of the king Ahab and afterwards he followed the teaching of Elias and had apparently some miracles for Bani Israel in Ariyha أريحا and elsewhere. And he died during the reign of the king يوءاش Jehoash (?) around 840 B.C. and he was buried in Samara.
وهو ابن ( شافاط ) من أهل ( آبل محولة ) . كان فلاحا فاصطفاه الله للنبوءة على يد الرسول إلياس في مدة ( آخاب ) وصحب إلياس . ولما رفع إلياس لازم سيرة إلياس وظهرت له معجزات لبني إسرائيل في ( أريحا ) وغيرها . وتوفي في مدة الملك ( يوءاش ) ملك إسرائيل وكانت وفاته سنة أربعين وثمانمائة 840 قبل المسيح ودفن بالسامرة . والألف واللام في اليسع من أصل الكلمة ، ولكن الهمزة عوملت معاملة همزة الوصل للتخفيف فأشبه الاسم الذي تدخل عليه اللام التي للمح الأصل مثل العباس ، وما هي منها .
he also added that the "ال" of the name are (the same as the) original (hebrew). This statement is a bit discuessed among scholars as al-Qushayru says that "ال" has been added as one can find in tafsir at-Tabari!
Differences in the Qiraat:
In the Quran Readings the majority read his name اليسع with a sukun on the "lam, ل" (this lam is silent), but among the Kufi's al-Kissa-i الكسائي and Hamza حمزة and Khalaf خلف read it الليسع al-layasa' with a shida on the 2nd (not silent but with a doubled consonant) "lam, ل". They used this pronunciation to make the name sound more like a non-Arabic name according to Imam at-Tabari!
- Al-Qurtobi added to this: that Al-Yas'a was a companion of Elyas (so they are different as the Quran quotes each of them in the same Verse) and they both lived before Zakaria, Yahya and 'Issa (Peace be upon them). Soem pretended that Elias is Idriss but this isn't true as Idriss was a Grandfather of Noh and Elyas was an offspring of Noh. Some pretended that Elias or Al-Yasa' is/was al_Khidr...
And Allah knows best.