Long ago (2014) there was a coin called summercoin. It had a limited x11 pow period and after the initial pump and dump the dev abandoned it and everyone lost interest. It was just another p&d coin soon to be forgotten.

Then soopy came from nowhere and decided to revive the project by switching to a new code base, swapping all the old coins for new ones and starting a new pow (x13) period for more coins. After that, it went full pos.
AFAIK there was no preimine

Since development was meant to continue with big plans, we needed a serious name. The name navajo was chosen with a vote, along with the logo. The name was inspired because of their contribution to WW2 with their "code" language.
The coin then rebranded

Then some people claimed that the Navajo tribe was not happy with their brand name being used like that. I'm not sure how founded the claims were but in any case, in order to avoid potential problems, after a long time, it was decided to rebrand yet again.
In order to keep it as simple as possible, the name was shortened to NAV, so no changes were required for exchanges.

Inflation is actually less than 5% in practice because many people do not stake. 5% would be the maximum if everyone did