This name of Lord Shankar is full of spiritual references. This name is common in Shiva-names and Vishnu-names both. The absolute Lord Shiva has entered in the heart of all living beings as Antaryami. Shipi means sea-shell and Visht means— to enter. One who could enter into a sea-shell, that is called Shipi-Visht. This shell is none other than the individual self (Jiva), which is tied with ignorance. Shiva is known as Shipi-Visht, as he resides in the heart of all Jivas as Antaryami.

If we relate this word to Vishnu, then Shipi-Visht means Shiva who possesses the form of Vishnu. The name Hari is also grasped with same notion. Theoretically Shiva is Jiva himself, because Sarvagya Muni, author of Sankshep Sharirkam, says— ब्रह्मैव संसरति मुच्यते च ।
The Taittiriya Samhita is accepted bona-fide as a guide to attain Vishnu. It says—

यज्ञो वै विष्णुः पशवः शिपि यज्ञ एव पशुषु प्रतितिष्ठति।

Another meaning of this name is—Lord Bhaskar, Sun-God. In Skand-Purana Sun-God is called as Shipi-Visht. Sun is also a direct deity of Lord Shankar. This name Shipi-Visht is found in Vedas—

नमो गिरिशयाय च शिपिविष्टाय च नमः।
Acharya Bhaskar Roy explains it in his Aalwal—
पशवः परमात्मनि श्रीविरहाद् द्विपदोऽपि नराश्च सुराः शिपय:।
तदनुग्रहकृदधृदयं प्रविशन्। प्रथितोऽसि विभो! शिपिविष्ट इति॥

Purport: O Lord! Two handed creatures like humans or celestials are like animals due to their spiritual ignorance. They are compared to sea-shells. Our of compassion You enter in their heart. Therefore you are called Shipi-Visht. Shruti tells that one who think that Shiva is separate, he is surely an animal. If Shiva was not associated with us, then we would have been inert and transient.

For protection of all creatures, Shankaracharya sites a beautiful prayer at the feet of Lord Shipi-Visht—

क्रीडार्थं सृजसि प्रपञ्चमखिलं क्रीडामृगास्ते जनाः
यत्कर्माचरितं मया च भवतः प्रीत्यै भवत्वेव तत्।
शम्भो स्वस्य कुतूहलस्य करणं मच्चेष्टितं निश्चितं
तस्मान्मामकरक्षणं पशुपते कर्तव्यमेव त्वया॥

Purport: O Lord Shambhu! You create this world just to perform your sweet sports. All the living beings in the world, they are like deers for your plays. Therefore O Lord! Whatever actions I have done after coming to this earth planet, they all must be aimed for your pleasure alone. O Lord Pashupate! My all deeds are tricky and selfish. So you alone hold the responsibility of my deliverance. Identifying the absolute nature of the self is true form of worship of Shipi-Visht.