Illus' name is never given in the graphic novels, animated series or tie-in books.
Since she strongly resembles the giant Valfreya (the only diference being that Valfreya has long hair), and because she was not listed as a seperate giant on the pages detailing the Giants of Old in Hilda and the Midnight Giant, it was initially believed that she was Valfreya. Her real name was finally revealed in Hilda's Book of Beasts and Spirits, in the section about giants.
In "Hilda and the Hidden People", Illus was known as "Bobblehat Mountain" before waking up. The graphic novel and animated series don't use this name.
Illus belongs to a race of ancient giants, that were the first creatures to live in the valleys.
When her friend Jorgen was tasked with guarding the Earth from the top of the tallest mountain in the North, she promised to meet him in the valley after his duty was over.
Sadly, as time moved on, the giants got into conflicts with humans, and were eventually forced to leave the Earth. Not wanting to leave without Jorgen, Illus kept waiting. Eventually, she fell asleep and over time her sleeping body got covered in snow and dirt, making it look like a mountain. The Elf King even build his castle on this mountain.
When Hilda visited the Elf King, she accidentally woke up Illus, allowing her to finally reunite with Jorgen. Afterwards, the two decided to follow their fellow giants into space.