The English word Dravidian was first employed by Robert Caldwell in his book of comparative Dravidian grammar based on the usage of the Sanskrit word "drāvida" in the work "Tantravārttika" by (Zvelebil 1990:xx). Caldwell coined the term "Dravidian" from the Sanskrit "drāvida", which was used in an 8th-century text to refer to South India by Adi Shankara. The publication of the "Dravidian etymological dictionary" by T. Burrow and M. B. Emeneau was a landmark event in Dravidian linguistics.
As for the origin of the Sanskrit word ', there have been various theories proposed. Basically the theories are about the direction of derivation between ' and '. That is to say, while linguists such as Zvelebil assert that the direction is ' >"" (ibid. page xxi), others state that the name "Dravida" also forms the root of the word "Tamil" (Dravida -> Dramila -> Tamizha or Tamil). 

The word "Dravida" may also have its origin from Sanskrit 'Drava' - meaning water or sea. The word Dravidian may have been used to identify people living in India close to the sea. Since southern India is surrounded by sea on three sides, the word may been used predominantly to identify the inhabitants of these areas.

There is no definite philological and linguistic basis for asserting unilaterally that the name "Dravida" also forms the origin of the word "Tamil" (Dravida -> Dramila -> Tamizha or Tamil). Zvelebil cites the forms such as "dramila" (in 's Sanskrit work "Avanisundarīkathā") ' (found in Ceylonese chronicle Mahavamsa) and then goes on to say (ibid. page xxi): "The forms '/"damila" almost certainly provide a connection of "dr(a/ā)" " and "... ' < ' ...whereby the further development might have been *' > *' > ""- / "damila"- and further, with the intrusive, 'hypercorrect' (or perhaps analogical) -"r"-, into "dr(a/ā)". The -"m"-/-"v"- alternation is a common enough phenomenon in Dravidian phonology" (Zvelebil 1990:xxi)
Zvelebil in his earlier treatise (Zvelebil 1975: p53) states: "It is obvious that the Sanskrit "dr(a/ā)", Pali "damila", ' and Prakrit "d(a/ā)" are all etymologically connected with '" and further remarks "The "r" in "" > "dr(a/ā)" is a hypercorrect insertion, cf. an analogical case of DED 1033 Ta. "kamuku", Tu."kangu" "areca nut": Skt. "kramu(ka)".".
Further, another eminent Dravidian linguist Bhadriraju Krishnamurti in his book "Dravidian Languages" (Krishnamurti 2003:p2, footnote 2) states:
"Joseph (1989: IJDL 18.2:134-42) gives extensive references for the use of the term ', "dramila" first as the name of a people, then of a country. Sinhala inscriptions BCE [Before Christian Era] cite '-, "damela"- denoting Tamil merchants. Early Buddhist and Jaina sources used '- to refer to a people of in south India (presumably Tamil); '- was a southern non-Aryan country; '-, ', and '- were used as variants to designate a country in the south (', "Kādambarī", "Daśakumāracarita-", fourth to seventh centuries CE) (1989: 134-8). It appears that '- was older than '- which could be its Sanskritization."

Based on what Krishnamurti states referring to a scholarly paper published in the International Journal of Dravidian Linguistics the Sanskrit word ' itself is later than ' since the dates for the forms with -r- are centuries later than the dates for the forms without -r- (', '-, "damela"- etc.). So it is clear that it is difficult to maintain Dravida -> Dramila -> Tamizha or Tamil.

मूळ/उगम
वांशिक ओळख
"द्राविडी लोकां"ची संकल्पना
Etymology