That Israel is called “Israel” is a matter of custom, not law. Unlike Israel's national anthem, national symbol, or national flag, there is no law officially setting the State of Israel's name as the “State of Israel.”
The only place where that term is used is in the Declaration of Independence, but that is not a legal document in the sense that a Knesset law is. A bylaw of the Law on Government states that the name “Israel” should be used on documents where the term “Palestine” had been used in the past, but that, too, does not mean that the name of the state is officially “Israel.”
That is set to change in the near future. Likud MK Oren Hazan on Sunday presented a law to officially designate the state's name to the Ministerial Law Committee, where it passed without objection. According to Hazan, “the purpose of this law is to prevent damage to the name of the state. To protect it we must legislate it to ensure that it is not misused.”
Currently – theoretically, of course – any private body could purport to represent the “State of Israel,” even if it does not represent the government or people of Israel. Under the new law, the term would be reserved for use only by official elected or appointed representatives of the state, as defined in the Basic Law on government.