TIL the word is actually from Hindi - I was all ready to object to your giving them the same name (if only I'd known what the Hindu one was called, assuming it was different) - I thought they were entirely unrelated symbols and ideas that just happened to have a similar representation.
Seems obvious in retrospect, knowing स्वस्थ ('svast'/'swast' meaning healthy) though I suppose being British/born (decades) post-war my association for 'swastika' are just not anything to do with well-being at all.
If you're objecting to me associating it to being British-born post-Nazism.. well, I spent a lot more time in school learning about the war and war-adjacent topics than I did Hinduism. And I don't recall the svastika from what I did learn about Hinduism at all. (I'm aware of it through film and reading.)
If I saw it in the street or as a tattoo (which I never have, aside from that depicted in American film and television) I would assume Nazism, unless it had dots or perhaps if it wasn't at an angle (or in film, obviously not if it's Bollywood). And the connotation of that isn't 'well-being' to me; I don't doubt (now, knowing the common origin) that's why they chose it, I'm simply explaining how I'd failed to make the connection.
> my association for 'swastika' are just not anything to do with well-being at all
Or if this is being misinterpreted - to be absolutely clear, I mean the word, as rendered in the English alphabet. I have absolutely no problem with it being used as a positive symbol, a स्वस्तिका, all I meant was that I didn't realise there was any connection at all! I thought there was one with positive associations, and one with negative, and they just looked similar but that was that.