Why is Shiva called Bholenath? What does it mean by Bholenath? Please explain story too if exists.
Why is Shiva also called Bhootnath, Amarnath, Kedarnath, Omakara etc.?
What does it mean by kedar?
As discussed in answer here Kedara is name of mountain and when Lord Shiva got established there he came to be known as Kedarnath:
यदि प्रसन्नेो देवेश ! यदि देयो वरस्त्वया।
स्थीयतां स्वेन रूपेण पूजार्थं शङ्कर! स्वयम्।। ६ ।।
Nara-Nārāyana said, “O Lord of gods, in case you are pleased with us and intend to bestow a boon, then you stay here forever for our adoration.
इत्युक्तस्तु तदा ताभ्यां केदारे हिमसंश्रये।
स्वयं च शङ्करस्तस्थौ ज्योतीरूपो महेश्वरः।।७।।
Sūta said, “When both of them thus spoke, Shiva got himself established over the snow clad Kedara mountain, in Jyotirlinga.
Hence Lord Shiva is called Kedarnath.
SataRudriya in 8th Anuvaka states:
नमस्ताराय च । [YajurVeda 16.40]
Salutation to him who is in the form of Pranava.
Similarly Atharvasiras states:
अथ कस्मादुच्यत ओङ्कारो यस्मादुच्चार्यमाण एव
प्राणानूर्ध्वमुत्क्रामयति तस्मादुच्यते ओङ्कारः ।
Why he (Rudra) is called Omkara? Because he sends the souls upward, at the time of dissolution.
Similarly Taittariya Aranyaka Yajurveda states:
ब्रह्माधिपतिर्ब्रह्मणोऽधिपतिर्ब्रह्मा शिवो मे अस्तु सदाशिवोम् [T.A 10.21]
the preserver of the Vedas and the one overlord of Hiranyagarbha, be benign to me. I am the Sadasiva described thus and denoted by Pranava.
Also as discussed in answer here there is a Jyotirlinga named Omkareshwara:
Situated in the banks of River Narmada on the Mandhata (Shivapuri) Island formed in the shape of OM in Sanskrit, Omkareswar is one of the Jyotirlingas besides another Amareswar Linga.
So, Lord Shiva is called Omkara.
Bhootnath has two meanings one is Lord of all beings and another is Lord of Ghosts.
SataRudriya hymn of Yajurveda states:
यो भूतानामधिपतयो [YajurVeda 16.59]
he who is Adhipati (Lord) of all beings.
And as I discuss in my answer here Lord Shiva likes Ghosts and is Lord of Ghosts hence called Bhootanath.
I do not like, O goddess, to reside anywhere without those ghostly creatures being by my side. Hence, the crematorium is a sacred abode to me. Indeed, O auspicious lady, it seems to me to be the very heaven. Highly sacred and possessed of great merit, the crematorium is much applauded by persons desirous of having holy abodes.'
So, Lord Shiva is called Bhootnath.
According to a Hindu legend, this is the cave where Shiva explained the secret of life and eternity to his divine consort, Parvati. Two other ice formations represent Parvati and Shiva's son, Ganesha.
त्र्यम्बकं यजामहे सुगन्धिं पुष्टिवर्धनम्
उर्वारुकमिव बन्धनान्मृत्योर्मुक्षीय माऽमृतात् ।।
We worship the Three-eyed Lord who is fragrant and who nourishes and nurtures all beings. As is the ripened cucumber freed from its bondage (to the creeper), may He liberate us from death for the sake of immortality.
सद्योजातं प्रपद्यामि सद्योजाताय वै नमो नमः।
भवे भवे नाति भवे भवस्व मां भवोद्भवाय नमः॥
I take refuge in Sadyojata. Verily I salute Sadyojata again and again. O Sadyojata, do not consign me to repeated birth; lead me beyond birth, into the state of bliss and liberation. I bow down to Him who is the source of transmigratory existence.
Hence Lord Shiva is called Amarnath.
Bholenath means Lord of the Innocents or The Innocent Lord or Lord who is easily pleased. We can find this attribute of Lord Shiva in various stories:
Also as described in this chapter of Srimad Bhagvatam Lord Shiva gives boon to Vrikasura:
So Vṛka decided to commit suicide by cutting off his head. Just at the critical moment, Lord Shiva appeared from the sacrificial fire and stopped him, offering the demon whatever boon he chose. Vṛka said, “May death come to whomever I touch upon the head with my hand.” Lord Shiva was obliged to fulfill this request, and at once the wicked Vṛka tried to test the benediction by putting his hand on the lord’s head.
As discussed in question here Lord Shiva granted fruit of his worship to a hunter although he was not aware that he was worshipping Maheswara:
To pass the time, he engaged himself in plucking the Bael leaves and dropping them down onto the ground. The next day he returned home and bought some food for himself and his family. The moment he was about to break his fast a stranger came to him, begging for food. He served the food first to stranger and only ate afterward. At the time of his death, he saw two messengers of Lord Shiva, sent to conduct his soul to the abode of Shiva. He learnt then for the first time of the great merit he had earned by unconscious worship of Shiva during the night of Maha Shivaratri.
Similarly as discussed in question here there is also this story of Kubera:
Another rather more romantic version is that one day Kubera had gone to rob a temple of Shiva, who is the king of robbers. During the robbery Kubera's taper had somehow been blown out. No matter how hard the dwarf tried he could not relight the taper. Nevertheless, he persisted with his efforts no matter how nefarious they were and, on the tenth attempt, he succeeded. Shiva is a benign god who is often pleased by the most illogical of efforts. This perseverance of Kubera's in his attempt to rob the god's temple won him much admiration from Shiva who subsequently granted the dwarf access to the Hindu pantheon of gods.
Hence Lord Shiva is called Bholenath.
It is believed that Shiva is easily pleased/glad by devotion. Also it can be considered as the lord of simple-hearted or innocent perople. So, Shiva is also called Bholenath. Bhootnath means the lord of bhoot.
You can read story of Bhasmasur and various Devas and Danavas that are graced (or pleased) from Shiva.