The name is referred to in Rg Vedam first , the oldest of VedAs .The exact quotation is "Gaam gathasya tava dhAma VaishNavam ". The effulgence of the Lord ( Svayam Jyothi) is being saluted here .He is param JyOthi .
(2)The nigantu explanation is " VishNurdEvathAsya tasyEdham vaa aNN) or that relates to VishNu .
(3)It is also the noun of the asterism "SravaNaa". SravaNam is VishNu's constellation ( SravaNa VenkatEsan ). Although SravaNa nakshthram is the celebrated constellation assoicated with Him , we have to remember the slOkam used by the AarAdhakar at Ahobila matam before ThiruvArAdhanam :
Thithir VishNus tathA vaara: Nakshathram VishNurEva cha yOgasccha karanam chaiva SARVAM VISHNU MAYAM JAGATH
(4)Vaishnavam also means the celestial residence of MahA VishNu (i-e) VaikuNtam .
(5)Finally , VaishNavam means the ashes of a burnt offering like in PurNAhUthi during a Vedic yAgam . (see Rituals) about those Yaagams , where cooked Havis is offered to Agni invoking devathAs , whose antharyAmi is MahA VishNu /Sriman naarAyaNA . We are back to Veda sambhandham now .
Vaishnavam can not be understood without knowing about VaishNava lakshaNam .That is a deep subject
Sri Vaishnavas can come from any caste (e.g) Alvars. Kulasekara was a Kshatruiya. Thirumangai was also a Kshatriya by birth. Nammalwar was not a Brahmin. Thirumazhisai Alwar was a Siva Worshipper earlier. Thondaradipodi, Periyalwar were Brahmins. The common things that tie them are the observance of the sacraments of Vaishnavism and the observance of the religious duties of Vaishnavas.DR.S.M.S.Chari"s well-written book "Vaishnavism, Its philosophy, theology and religious discipline" will be very helpful to you to gain a perspective on the details of Vaishnavism. Chapters 8 and 13 are brilliant summaries of two important doctrines of Vaishnavism. Chapter 8 deals with Vishnu and Goddess Sri. Chapter 13 deals with the important subject of Prapatti.
Bhagavat Kainkarya and Bhagavata Kainkarya are the two types of worship. The first is the service to the Lord without expectation of rewards(Nishkama Karma described in Bhagavat Gita.) The Panchakala Prikriya or the five fold daily religious duties can be folded in to the Bhagavat Kainkarya.
The second type of Kainkarya is known as Bhagavata Kainkaryam or service to Godly men and women.Bhagavata Kainkarya is recognized as one of the supreme virtues of a true Vaishnava. The reasoning is as follows: True devotees of Vishnu (the Bhagavatas) are very dear to the supreme Lord, Vishnu(Sriman Narayana). Any service rendered to his dear Bhagavatas are therefore most pleasing to Vishnu. DR. Chari has quoted in support of this view a passage from Padmottara Purana:" Of all the types of worship, the worship to Vishnu is great; Greater than that is the service to Bhagavatas." Service to Bhagavatas can take many forms: providing food, shelter, clothing et al.Bhagavata apachara or offence to Bhagavatas is to be avoided at all costs, since, it brings the wrath of Bhagavan.
Out of his infinite mercy, Acharya Ramanauja has suggested 5 Kainkaryas to suit the competence and convineience of the Vaishanvas; (1) study of Sri Bhashya, the commentary on Brahma Sutras (2) for those, who find it difficult, study of the Naalaiyra Divya Prabhandam (3) for those , who can not do that, services to Vaishnava divya desams and Abhimana sthalas thru provision of Food, Flowers or lighting of lamps (4) For those, who can not afford that the mantra Japa of Dwayam, the sacred Mantram on Narayana and Sri Devi. (5) For those, who feel they can not follow any one of the above four Kainkaryas, The company of Vaishnavas is recommended as a last resort. Ramanuja's prescriptions cover the entire world of Literate scholars in Sanskrit and Tamil as well as illiterate masses, who have embraced Vaishnavism. No one is thus left out.
See also Brahmin Iyengar