Modern Tamil has loanwords from all sorts of languages, wouldn't be surprised if orange also fell into that list.

In Malayalam, lemon is naaranga. Local sweet varieties are called madhura naaranga or sweet lemon, where interestingly the former half is tatsama (as-is) Sansktri and latter pure Dravidian. Almost all citrus fruits have the naara root. This must be the same in Tamil too, except that it is usually free of tatsama Sanskrit terms.

The oranges that are commercially sold must be sweeter cultivars introduced later on, after English adoption, because of which we ended up calling these oranges.

Edit: Even Tamil is the English term for Thamizh.