The name Juni is a girl's name of Scandinavian, Finnish, Swedish origin meaning "June". Juni and is often added to lists like Girl Names Uncommon in the US and discussed in our forums with posts like "Rate the Previous Signature!".
From the experts:
Juni is the Swedish, Norwegian, Danish, and Finnish form of the month name June. While Juni feels cute and fresh, most Americans would assume it was a nickname or a Joni variation. We prefer Juna or the English June.