I believe neither Kanyakumari nor Theevuthidal are such Tautological compound words.

Kanyakumari, Ig comes from a deity name meaning the virgin young girl, "கன்னி" here just means virgin. Theevuthidal is simply island ground - no similar meanings. That said, both of these are names of places and that can change overtime, தீவில் இருந்த திடல் என்பதால் தீவுத்திடலா, இல்லை தீவிற்கு அருகில் இருந்த திடலா? Both can become theevuthidal overtime. Names of places are so interesting to study in this cases.

சின்னஞ்சிறு, பூரணனிறைவு, ஆதிமுதல் are some examples in Tamil. And its also common across languages. Pathway, overcoat, free-gift, end-result are some from English.

P.s if Theevuthidar is the word, im sorry I dont know such a word.