I am a Hindu Nair (https://en.wikipedia.org/wiki/Nair). There is also a sub caste-I don't know which one it is. Both my parents are Nairs, but belonging to different sub castes I think.

As for offensiveness, I don't remember anybody asking me about my caste (outside of govt forms-they need it for job/educational reservations) except once. He (an Indian from my state) didn't ask me my caste, he heard my name and immediately said "oh you are a Nair" and I felt really weird and wanted to end the conversation quickly. If a foreigner asks me, I don't think I would mind. I am not sure if I would be comfortable if an Indian asks me though.

Another Hindu Nair here; it’s not offensive to ask, only discriminate.

Nair is actually included in my name so you get the caste info just by getting my name.

I feel it's offensive. But a foreigner may do so out of curiosity and ignorance so I can't be angry about it.