We were discussing names in class and we wanted to know if Eretz-Israel was the official name of Israel in its constitution, etc.
Israel does not have a written constitution, but it has a constitution drafting project on its website. On this website, its declaration of independence states: “and its executive organ…shall be the Provisional Government of the Jewish State, to be called ‘Israel’.”
Thus, the official name is the state of Israel as per the Israeli government’s website: https://knesset.gov.il/constitution/ConstIntro_eng.htm
However, in that same declaration document, it does reference the name Eretz-Israel. Specifically, it says: “[…]hereby declare the establishment of a Jewish State in Eretz-Israel, to be known as the state of Israel.”
This is from the Israeli government’s website: https://www.gov.il/en/Departments/General/declaration-of-establishment-state-of-israel
(Edit: Corrected below to note the official name under the British as Mandatory Palestine alongside supposed translation differences for the name) In the past, Eretz-Israel was an official name under the British Mandate as per the Jewish Virtual Library (and the website has some reasons for the name of Israel): https://www.jewishvirtuallibrary.org/why-the-name-israel
Edited below to correct final point on British Mandate:
Under the British Mandate, the official name was Mandatory Palestine. However, sources online seem to point that there is a language difference (including the Jewish Virtual Library linked above) that denotes how the official name was translated into Arabic and Hebrew. These sources say that in Arabic, it was still known as Palestine: فلسطين . This romanized is “Filasṭīn.” While in Hebrew it was known as: פָּלֶשְׂתִּינָה (א”י). This romanized is Pālēśtīnā Aleph Yud or Pālēśtīnā (E.Y.) where Aleph Yud/E.Y. stands for Eretz-Israel (Eretz Yisrael), which would make it Palestine Eretz-Israel in Hebrew. However, this is difficult to truly determine without knowing Hebrew since the secondary sources online do not seem to note a primary source that translated the name as such during the time of the British Mandate. An Israeli library website does have a map of Mandatory Palestine where its name does include Aleph Yud in the map: https://lib.cet.ac.il/pages/item.asp?item=23047
But further sources will have to be found and positioned correctly in history to fully confirm this.