Mainform 3 :

As Bhairava, Shiva has 64 forms. In this form his hair is depicted like flames coming out from his head. He has a dog as a companion. He is naked, his body smeared with ashes and is roaming all over. Sometimes he is depicted with skulls and snakes while dancing on cremation places and beating demons.

Riding animal / animal who accompanies:
Dog.
A dog is the guardian of the underworld. A dog symbolizes also uncleanness

Myth about roaming Shiva:

Sarawati was the daughter of Brahma. When Brahma saw the beauty of Saraswati he became amorous. To escape from her father’s passionate approach Saraswati ran to the lands in all four directions and to heaven, but she could not escape from her father. Brahma
Brahma, in his obsession, sprouted five heads, so that he could look upon her at all times. To restrain his lust, Shiva as the ferocious Bhairava wrenched off one of his heads.

As penalty Shiva had to roam the entire universe with the skull of Brahma in his hand.
Eventually he was forgiven after bathing in the holy pond in Varanasi.
In the form of roaming Shiva, he is Kankala- Murti.