What is the name of fluorescent stone from Dawnguard expansion?

It is more connected with the world lore but I think someone might it find interesting.

Is there any information about this stones in books or from NPCs? What is the name of it?

The technical answer to this questions is: The game does not directly specify what this is.

However, the community seems to feel that the most likely answer is that this is raw Aetherium:

https://elderscrolls.fandom.com/wiki/Aetherium

As the article notes:

Sometime after 1E 221, the Dwemer of Skyrim discovered a considerable source of raw Aetherium in Blackreach.

However, the referenced items for that (Katrina's Journal and The Aetherium Wars) do not directly state that the glowing mineral formations are indeed raw Aetherium. Still, it is a reasonable interpretation as The Aetherium Wars states that:

Modern scholars know Aetherium as a rare, luminescent blue crystal found in some Dwemer ruins.

Obviously, your picture above is a luminescent blue crystal, so it's not unreasonable to say "it's, for sure, Aetherium". But, still, there's no direct statement of that anywhere in the game.

It's likely the type of stone Soul Gems are made of. You'll likely find a Geode Vein near those.