Since war of 5 kings has become not accurate by twow, how would you name the years from 298? And the 2nd coming of the others ? Another war or a part of this great conflict ?

It is in the nature of historians to be pedantic about periodization and labelling, but I would argue that we should stick with the name. 

1. It’s already in common use, so it’s a term that people will understand when historians use it, whereas they might not understand a new term which isn’t much used. 
2. The name speaks to the unusual nature of this Westerosi civil war, that rather than a fight between two factions over the succession as was the case in the Dance and the Blackfyre Rebellions, you have many sides, not all of whom are interested in the Iron Throne but all of whom ultimately claim royal status.
3. It’s not uncommon for names to be not quite accurate when it comes to complicated conflicts. For example, the War of Jenkin’s Ear is technically part of the War of Austrian Succession, but in the former Britain and Spain were not fighting over the succession of Archduchess Maria Teresa and in the latter, no one was fighting because Spanish coast goards cut off the ear of a British smuggler. 

As to the War for the Dawn, I think it will be seen as a second conflict, as the cause, sides, conflict zones, etc. will be distinctly different from the War of the Five Kings.