This name is much alike Rameshwar, because it implies a dual meaning— most beloved of Lord Vishnu, that Vishnu-Vallabh; or Vishnu is most dear to whom that Vishnu-Vallabh. How can one describe the affection between Vishnu and Shankar, as their form is one and the same. Stories depicting friendship of Vishnu and Shiva, are spread all over the Puranas. They can not live without each other. Their friendship is so intense, that Shankar rejected the request of other Gods for his personal marriage, but he accepted it when requested by Vishnu. Moreover, the philosophers conclude that Lord Vishnu always meditates upon Lord Shiva, while Shiva meditates upon Vishnu eternally. It is also mentioned within context of Mother Sati in Ramayana.

Lord Shankar says—“ Vishnu is my heart and I am heart of Vishnu.” As the body may not survive without heart, so they can not remain without each other. Because Vishnu is nothing but a manifestation of Shiva’s half body, therefore Shiva directly holds Vishnu on his left.

Shiva eternally resides in the heart of Vishnu. Once demigods went to mount Kailash, but they could not found Lord Shankar there. Then they approached Lord Vishnu and told about the missing of Shankar. Lotus-eyed Vishnu said that Shankar is merrily relaxing in my heart, and he drew out Shankar from his heart and showed to demigods. Vaaman-Purana states—

तमूचुर्नैव पश्यामस्त्वत्तो वै त्रिपुरान्तकम्।
सत्यं वद सुरेशान! महेशानः क्व तिष्ठति॥
ततोऽव्ययात्मा स हरिः स्वहृत्पंकजशायिनम्।
दर्शयामास देवानां मुरारिर्लिंगमैश्वरम्॥

Vishnu asked a benediction of firm devotion from Lord Shankar.  It is mentioned in Saur-Purana —

भगवन् देवदेवेश परमात्मन् शिवाव्यय।
निश्चला त्वयि मे भक्तिः भवत्विति वरो मम॥

According to Harivansha-Purana, Krishna performed great austerities for twelve years at Kailash mountain. Then he  saw  Lord Sadashiva. Being pleased by chanting of Namah Shivaya, Shankar granted him a boon, to get a son.

Vishnu has enormous love for Lord Shiva, so he is ready to do anything for Shiva. When a plan was worked out to kill Tripurasura, the mother earth turned herself into a chariot, but demigods could not control it. Then Vishnu assumed the form of a bull and personally pulled the chariot. Lord Shankar was looking for a arrow, which could be infallible in killing of Tripurasura. Then Vishnu moved to the hands of Shiva, expanding himself as an arrow. To know the origin of Shivalingam, Vishnu adopted a pig-form. He became a beautiful maiden in the form of Mohini, and enchanted Lord Mahadeva. Whenever Lord Shankar wishes for dance, Krishna plays  kettledrum for him. Out of his jolly nature, Rasabihari often becomes a female friend of Shiva. While worshipping Lord Shiva with thousands of lotuses, sometimes he offers even his lotus-like eye at Shiva’s feet. So what to speak about the loving devotion of Vishnu towards Shankar. Below is a wonderful  description in the words of Shankaracharya—

बाणत्वं वृषभत्वमर्धवपुषा भार्यात्वमार्यापते।
घोणित्वं सखिता मृदंगवहताचेत्यादिरूपंदधौ।
त्वत्पादेनयनार्पणंचकृतवांस्त्वद्देहभागोहरिः
पूज्यात्पूज्यतरः स एवहिनचेत्कोवातदन्योऽधिक:॥

Bhaskar Roy says that you are Vishnu-Vallabh, because you gave the weapon called Sudarshan Chakra to Vishnu, who was fixed in penances to please you.

वितरन् हरये तपस्यते पदरेखाजनितं सुदर्शनम्।
वपुरर्धमपि प्रियाय ते प्रथितस्त्वं भुवि विष्णुवल्लभः॥

In spiritual science, Vishnu is known as material cause (Upadaan) and Shakti as efficient cause (Nimitta), and Shiva is origin and support of both. Naturally the material cause (Vishnu) would love its origin, because it can not stand without Shiva’s  support.

Both of them are so much identical that Vishnu got black and Shiva white, by contemplating on each other. Thus Vishnu’s quality of goodness entered into Shiva and Shiva’s quality of ignorance entered into Vishnu. Consequently Shiva is always busy in meditation and Vishnu in deep slumber. To identify the non-dual nature of the world is the true form of worship of Vishnu-Vallabh.