We can use "THAMIZH" instead of "TAMIL" to pronounce it. It is more suitable to pronounce the word "TAMIL". "IL" is not good as the sound in "IZH". In your name also you can see it.
Practice makes perfect..
people in tamil nadu pronounce the word 'tamil' as 'Thamizh' only while they speak in tamil. But once you talk in english your accent changes and you need to pronounce it as tamil. It is because the English language is not having that sound. (In English language there are only 46 sounds). So according to every language the slang changes. for example some english names "peter" is called as 'Pethuru' in tamil.
we call the Telungu Language as 'Telungu'. Where as the correct pronunciation of the language is "Telugu". so for every language according to the slang and accent the pronunciation differs.
Defeat the defeat, before the defeat defeats you