As seen on wikipedia:
Bettina is a female name of Hebrew and Latin origins predominantly found in the Italian and German languages. Pronounced BahTeeNah, this name has various interpreted meanings.
Bettina can be found in the Italian language originating from the name Benedetta. Benedetta is the feminine form of Benedict which means blessed. (M-Benedetto/L-Benedictus/E-Benedict). The German version of Bettina comes from the Hebrew name Elizabeth. In its older form Elizabeth was known as Elisheba and Elisheva.
Many sources will claim that Bettina has origins in various cultures such as Greece, The Netherlands, Russia etc. However this is not the case. This is generally due to the false attribution to Elizabeth. The name Elizabeth permeates nearly every western language. The fact that one can find the name Elizabeth in most European cultures, leads some sources to mistakenly attribute the etymology of Bettina (its diminutive) to those cultures. The name Elizabeth can be found in a culture, ergo Bettina must come from that culture as well. This is just not the case. And this is the same reason Bettina is often mistakenly attributed to Elizabeth in the Italian culture instead of from where it is really derived: Benedetta.
Because it has two distinct origins, the name Bettina also has two distinct meanings that can be ascribed to it. The Italian version of Bettina basically means "Blessed". However the German meaning is not as simple. Due to its relatively ancient roots, the translation of the name has brought forth changes in its meaning. Some of the German interpretations are: God is my oath, consecrated to God, dedicated to God, oath to God, sacrificed to God, God's promise, etc. All very similar and all just slightly different.