The name was originally a diminutive form of the name Vilhelmiina, but later became an independent name in Finland due to its coincidental meaning of “pearl,” in Finnish. The pronunciation could be heard here: http://www.forvo.com/word/helmi/
As of 2011, Helmi was the 11th most popular female name among Finnish speakers in Finland.
The designated name-day in Finland and Estonia is May 7th. In Sweden, it is April 6th.