The name may have several different possible etymologies. Its most likely explanation is that it is a Frisian feminine form of Tamme.
It may very well be a feminine form of Tamino, which is the name of the main character in Wolfgang Amadeus Mozart’s The Magic Flute. In this case, the name is of uncertain origin and meaning and may been the invention of Mozart himself.
It could also be taken from the name of the river in Switzerland and an eastern valley in the Swiss Alps.
A similar name, Tahmina, is found in Persian mythology, as the name of the wife of Rostam and the mother of Sohrab. Tamina may be a Germanized form.
Currently, it is the 180th most popular female name in Germany, (2011).