Jai 1

I think there should probably be a Jai (1) and Jai (2) and one should be the name that originated in India and the other the one that originated in English speaking countries.

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Jai is popular in Australia (top 100, previously) and there are rugby players Jai Field and Jai Arrow and actor Jai Courtney (all Australian). They don't seem to have any Indian roots. I think it is a name that exists independently in India and then in Australia and other English speaking countries. [noted -ed]

Can be a girls name as well.

Jai (or Jay) means Victory in the Sanskrit language. I think of it now more of a English name. I live in Melbourne where I've heard that name too many times and everyone with the name was of Anglo descent.