I was also raised in kovai, although I was born in Chennai and lived elsewhere. Coimbatore as far as I know derives its name from its presiding deity Koniamman, whose original temple was banks of a river Siruvaaani famous even now for its sweet waters. Siruvaani was called Nallai or Nellai or something in those days. Anyway the city was named after Koniamman as Konia-muthoor and later became Coimbatore.
Prof. Ragahava iyengar in one of his books had pointed that since Kosar(people from Kosala country) settled here and created a new city it was called Kosar-putur, which in turn changed into koyambutur.
Happy to notice that the topic kindled many musings.
As far as I see it, I feel nations change names due to 2 reasons 1. Renaming cities has been one way in which countries has sought to reclaim national identity since throwing off colonial rule like Ceylon was changed to Sri Lanka to forget the British remnants and the name Sri Lanka is close to Sinhalese 2. Geographical reasons such as when 2 countries join and borders such as Tangayika and Zanzibar joined to become Tanzania.
The Chola empire came to power in 9th Century and remained till 13th century. They ruled most of South India, Sri Lanka, the Maldive Islands, and even parts of the Indonesian island of Java from their homeland near Thanjavur (Tanjore) on the southeastern coast of what is now Tamil Nadu, India.
Marcopolo, whose wrote expeditions in 1290 has renamed / called many countries in his mother tongue such as Ilamuridesam is at modern Aceh. ( Lamuri of the Arabs,Lambri of Marco Polo, Lan-Wuli or Lan-Li or Lan-po-li of Chinese records.).
He refers Andaman as "Angamanain "on his way home from his escapades in China. Legend says that Andamans got its name from the monkey headed god of the Hindus called Hanuman (in Malay Handuman) from the Hindu scriptures when he leaped from India to Thailand he stepped on Andamans.
The names we find in PS as Kadaram in Northern Malaya, Gangga Nagaram in Central Malaya. Kadaram is now a modern state of Kedah in Malysia. Gangga nagaram is Kota Gelanggi, far down south in the state of Johor (Malysia). Believe that names are changed due to integration of states and renamed to be close to their mother tongue Bahasa and Malay.