Jeztah, the explaination above (that since the article of the 1982 war is called 1982 Lebanon War and since that war only since 2006 has been called the First Lebanon War only in and to Israel, then this war should be called 2006 Lebanon War is incorrect and that logic is not supported by Wikipedia policy. The 2006 Lebanon has very little credentials (as I am proving above.) Israel-Hezbollah War carries no POV implications (the excuse George.Saliba named above is purely original and cannot be heard anywhere else in all seriousness.) Using his logic, 2006 Lebanon war would be incorrect since fighting began and took place in Israel as well. Israel-Hezbollah War meets the criteria of Rule #1 and #2. Neither George.Saliba nor any other editor has come close to proving another single name. And George.Saliba, "(c) it doesn't list the party that suffered the most death and destruction as a result of the conflict." Way to make up Wikipedia policy! I do not appreciate that at at all. You know as an editor that that is purely and totally irrelevant.  
I agree that "2006 Lebanon war" isn't perfect, but it is the closest to meeting Wikipedia policy we have found thus far. Also, the "(c) it doesn't list the party that suffered the most death and destruction as a result of the conflict." is entirely relevant to Wikipedia policy, per naming conventions rule #3. It becomes quickly apparent to anyone doing even the minimum amount of research that "Israel-Hezbollah war" doesn't meet rules #1 or #2. It might meet rule #3, though that is also disputable. —  [talk]