As I discuss in this answer, the Pancharatra Agamas are the foundational texts of Vaishnavism. Similarly, the foundational texts of Shaivism are known as the Shaiva Agamas, aka the Shaiva Tantras. My question is about a Shaiva Agama known as the Parakhya Tantra, which I discussed earlier here.
As I discuss in my question here, in the worldview of the Shaiva Agamas, the order of gods from lowest to highest is Brahma, Vishnu, Rudra, Maheshwara, and Sadashiva. They are said to govern the five functions of creation, preservation, destruction, obscuration, and revelation, and they correpond to the five heads of Sadashiva which I discuss here and here. In any case, in this excerpt from the Parakhya Tantra, the etymology of these five names is described:
Or rather (va) there is but one supreme Lord who has different forms (bhedaih sthitah) that are [different] in [no more than] their names (namagaih). [He is called] Brahma because he is great (brihattvat), because he fills (bramhakatvat) or because He possesses Brahman [va brahmayogatah]. He is called Vishnu because it is His nature to be powerful (prabhavashilatvat), because He is the source of the universe (prabhavo jagatah), He is omniscient (prabhuh). Because He drives away affliction (rujam dravayate) He is called Rudra, since the affliction is destroyed (rujah kshayat). Because He possesses all the attributes of sovereignty (sarvaishvaryagunashleshat), the sovereign Lord (ishvara) [is called] Mahesvara. He is Sadashiva [bexause he is] always favourable (sadakantah), or [because] Shiva means situated at rest. Thus there exists, called with various names, only one Lord of the universe.
Most of these etymologies make sense, or at least they conform to the standard pattern of etymologies in Hindu scripture, namely that the word being defined has some similarity in sounds to the word used to define it. But I'm interested in the etymologies given for the name "Vishnu".
The Parakhya Tantra connects Vishnu to three attributes: prabhavashilatvat or being powerful by his very nature, prabhavo jagatah or being the source or the Universe, and prabhu or being omniscient. But my question is, why do none of these definitions have anything resembling the sound of the name "Vishnu"? This is in contrast to the standard definition of Vishnu found in Yaska's Nirukta and elsewhere connecting Vishnu to the root Vish meaning to pervade, so that Vishnu means he who pervades all things.
Is it possible the Parakhya Tantra isn't providing an etymology for the name "Vishnu" as such, but rather the etymology of some other name of Vishnu? It could be Prabhu or something that starts with Prabhu, like Prabhava or Prabhakara. Does anyone know another scriptures tha give these definitions?