The river Kaveri was originally known as 'Kaverikanyaka' and
was brought from the mountains (Brahmagiri) by a Chola king.
There is mention of 'kaveri' in Thiruvalangadu copper plates in the context of
tracing the genealogy of Cholans.
She is 'kaverikanyaka'.
"(V. 35.) Having come to know that king Bhagiratha engrossed in penance brought down (from heaven) the river of gods (i.e., Ganga) (to earth), this king (also) desirous to fame brought her (i.e., Ganga) to his dominions under the name Kaverakanyaka (i.e., Kaveri).[1][25]"
the king mentioned here is Chithradhanvan.
The text of the inscriptions can be read at
also written in my blog
http://jayasreesaranathan.blogspot.com/2008/04/tretha-yuga-in-cholan-inscriptions.html
The Choodamani nigandu verse for kaveri is this.
"Ponni kaaviri irandum porundhu kaavEriyin peyar"
(5-22 , "Choodamani nigandu, moolamum, vuraiyum" 14th edition published in Kurodhana varusham (1925) by Vidhya anupaalana yandira shalai, Chenna- p-patinam)
Other names of KaavEri are given as 'ponni' and 'kaviri'.
What is kaa?
Verse 11-13 says:-
Kaa – kaa-venbathu thulaam, poonjolai, kaatthal, thOL sumai naarpere
Kaa has 4 synonyms.
Thulaam – balance,
Poonjolai – group of flowering plants
Kaatthal - protecting
ThOL sumai- Burden / weight on the shoulder.
Perhaps it is kaa+viri
since the river meanders through poonjolai (as in Srirangam)
'Kaa'-vai viritthu-k-kondu pOvadhaal kaaviri.
At Srirangapatna
But original name is kaveri – perhaps an idukuri-p-peyar.
Another input from this nigandu:
Kaveri is one of seven rivers of Bharatha varsha.
The 7 rivers are
Ganga
Yamuna
Narmada
Saraswathy
Kaveri
Kumari
Godhavari
Verse 12-74:-
"Vazhi gangai, yamunai, nanmadhai, saraswathy, kaaveri
vizhumiya kumari, Godhavari yEzhu nadhiyin pErE"
From this we understand that Kaaveri.had a special place as a Holy river and
was equally revered along with Saraswathy, Ganga etc.
She is one among the sacred seven.
Kaveri has been associated with bringing prosperity to the land.
"Vaan poippinum thaan poiyaa-k-kaveri"
is the oft repeated verse in Tamil poems of yore.