The name Jasmin is a girl's name of Persian origin. Jasmin and discussed in our forums with posts like "Think/Say".
From the experts:
Jasmin doesn't have the grace of Jasmine (which in 2016 ranked at 122 in the US Top 1000), but it is far more preferable to the trendier versions doing the rounds like Jazmin or Jazzmyn. If you are looking for a more unusual variant try Yasmin or Jessamine.