Reputations are earned sometimes over a long string of releases but sometimes it just takes one game to dramatically improve or tarnish that reputation.

One example is Uncharted 2 for Naughty Dog. Uncharted was a surprise hit. Crash and Jak series did well but it wasn't until Uncharted 2 became of one the highest rated games ever and swept GOTY awards that people started calling them Naughty Gods and realized they were one of Sony's best assets.

Another example is Demon Souls. From Software were barely know for Armored Core games. Enchanted Arms sucked. Boom Demon Souls was a surprise hit. They changed one word to create a new IP they could release on multiple platforms and their series are still going strong

A negative example would be Lair for Factor 5. Beginning of their downfall.

Haze, for Free Radical, in the negative sense. A terrible game from a studio that had turned in some of the best shooters of the 6th gen.

Too Human was a disaster for Silicon Knights, and that along with X-Men: Destiny killed them altogether.

I don't agree with your ND example... you said yourself they have been making their reputation since Crash, so it wasn't a single hit that made they famous...
You could say it about Minecraft and PUBG though.

Or even Bungie that with Halo jumped from 0 to 100 straight.

Team Sonic's reputation was not in its better days, but after 06 it sank to the bottom of the ocean, and hasn't recovered since.

Souls (specifically Dark Souls) put FromSoftware on everyone else's map and marked a string of high quality AAA titles with cult fanbases.

Uncharted 2 for Naughty Dog
Horizon for Guerrilla Games
The Witcher 3 for CD Projekt Red

True. Demons Souls completely changed FS's rep. They just reached a new fanbase and created a cult following. 

Retro and Metroid Prime - I remember at the time no one knew what to expect and I'm pretty sure it got mostly 9/10 scores while updating a beloved 2D game to 3D.

Blood Omen: Legacy of Kain and Eternal Darkness: Sanity's Requiem had pretty dedicated followings.