Shiva is known as Kailash-vasi because he resides on Mount Kailash. Actually Shiva loves to be in mountains. Generally ascetics have an special attachments with forests and hills because they find seclusion there. There is a Himalayan range of mountains In the northern section of India, and Kailash is a distinctive highland among Himalayan mountains. Because of the pure and peaceful vibrations of that sacred place, devotees are able to behold Lord Shiva-Parvati there. Gangadhar is named as Kailashwasi due to his residence on the top of that mountain. The rivers like Ganga, Sindhu, Brahmaputra etc are originated from Mount Kailash. Kailash means one which is white like crystal and its shade is spread all-over the water. Otherwise the romantic paraphernalia is also mentioned by the term ‘Kailash’. Shiva is always lying down in ecstasies of conjugal affairs, so he is called Kailashvasi.
Siddhant-sar-upanishad claims the ‘state of transcendence’ as the only meaning of Kailash— param kaivalyah sah eva kailashah. Hence, being fixed in the state of bliss aroused by self-realization is the actual sense of Shiva’s residence in Kailash. Acharya Bhaskar explains the meaning of Kailashvasi as under—

हरेर्मूर्ध्नि मेरौ हिमे मन्दराद्रौ भवेत्केलिभूमौ भवत्कर्मगम्याः।
तदूर्ध्वं परा ज्ञानलभ्यास्ति तासु स्थितत्त्वेन जातोऽसि कैलाशवासी॥

Purport: Your personal resorts which are achieved by actions, they are located at Meru mountain, Himachal mountain and mandar mountain, which are above the Vaikuntha planet. You are called as Kailashvasi because you dwell in those regions, and apart from it you also dwell in a region which is derived by knowledge only. According to Rahasya-Vidya Kailash mountain is situated within the Sahastrar-chakra (a thousand petalled lotus like chakra at the crown of the head, known as crown chakra) and that chakra is the abode of Lord Shvia. Realization of Shiva is the true sense of worship of Kailashvasi. This Kailash is beyond to all other planets including Vaikuntha etc.