Premise: Rina is a feminine given name with multiple origins. It is also a feminine name in the Sanskrit language meaning "melted" or "dissolved", and is also a Hebrew name meaning "song; joy". The name Rina is also a Russian hypocoristic for "Ekaterina" and is a feminine given name of Japanese origins, where it was proportionately used the most in the twentieth century.
Hypothesis: Sanskrit means "melted" or "dissolved."