Although "pranavah" occurs in vishnu sahasranama, it seems that the impersonal "Om" clashes with the "lakshmipati pitambaradhari shanka chakra gada pani" image of the God of vaishnavites.
According to what Sri Vaishnavism, the Pranava denotes the supreme Brahman. Here is what the Sri Vaishnava Ramanujacharya says in this section of the Sri Bhashya:
We therefore shortly explain the drift of the whole chapter as follows. At the outset of the reply given to Satyakâma there is mentioned, in addition to the highest (para) Brahman, a lower (apara) Brahman. This lower or effected (kârya) Brahman is distinguished as twofold, being connected either with this terrestrial world or yonder, non-terrestrial, world. Him who meditates on the Pranava as having one syllable, the text declares to obtain a reward in this world--he reaches the world of men. He, on the other hand, who meditates on the Pranava as having two syllables is said to obtain his reward in a super-terrestrial sphere--he reaches the woorld of the atmosphere. And he finally who, by means of the trisyllabic Pranava which denotes the highest Brahman, meditates on this very highest Brahman, is said to reach that Brahman, i. e. the supreme Person.--The object of seeing is thus none other than the highest Self.
He is referring to this chapter of the Prashna Upanishad, by the way. Also, the Sri Vaishnava Acharya Parashara Bhattar says that the "Pranavah" name in the Vishnu Sahasranamanam refers to the fact that the Pravana indicates the relationship between Jivatmas and Brahman:
By means of the sacred Pranava mantra, Bhagavan reveals to His devotees the true relationship between Him and them, and makes them understand the need for surrendering to Him.
For details on how the three syllables of the Pranava convey the relationship between Jivatmas and Brahman, see Vedanta Desikan's Rahasyatraya Sara.
Madhwas also think that the Pranava refers to Brahman. Here is what Madhvacharya says in his Mandukya Upanishad Bhashya:
Om is the designation of Brahman, and it is called Akshara or the imperishable also. For the word Om means literally "that by which everything is pervaded (otam)." Because this word is woven in Him, therefore Om denotes the Lord Hari.
And later on in the Mandukya Upanishad Bhashya, Madhvacharya gives an explanation for why Vishnu is called Pranava:
Vishnu in his four-fold aspect as Vishva etc. is called Pranava also; because he controls or leads (pranayana) the waking etc. states of the Jiva.