Shambhu is modified word from Swayam bhu which means "Self Born" and is another name of Brahman or Purush from Upanishads. No other Deity is called Shambhu or has a Nirakaar form like Shiva Lingam....
The meaning of shambhu is one who creates auspiciousness, Now if one speaks shambhu repeatedly it sounds like bhuSham which means ornament, which one can interpret as The lord shambhu is like the ornament of the world.
Shambhu from Sham (meaning peace) means "from whom peace is born" or "one who is the source of peace". Another name of Lord Shiva, Shankara, has a similar meaning- One who bestows Sham or peace. Shiva's meaning i think u know already- the auspicious one.
The other popular names associated with Shiva are Mahadev, Mahesh, Maheshwar, Shankar, Shambhu, Rudra, Har, Trilochan, Devendra (meaning Chief of the gods) and Trilokinath (meaning Lord of the three realms)
Here they are named Nirriti, Shambhu, Aparajita Mrigavyadha, Kapardi, Dahana, Khara, Ahirabradhya, Kapali, Pingala and Senani – the foremost. .. The Vishnu Purana narrates that Rudra – here identified with Shiva – was born from the anger of the creator-god Brahma.
Shanti, Shakti and Shambhu are signified by the three Nadas. Now as I discuss in this question, in the worldview of the Shaiva Agamas, the hierarchy of gods from lowest to highest is Brahma, Vishnu, Rudra, Maheshwara, and Sadashiva. So I assume the "Rudra, Ishvara, and Sadashiva" part is a reference to the last three names on that list.
Among all secrets, it is the supreme secret. O sage! In earlier times, Shambhu himself narrated this to Vishnu, his noble devotee. When he was asked with great devotion, he did this for the sake of benefit to others. After this, I asked the intelligent Vishnu, Shiva’s supreme devotee. O supreme among sages! Out of his love for me, he told me ...