The name Bernice in the Bible
When Paul was heard in Caesarea by king Agrippa the Second, Bernice was present (Acts 25:13). Bernice and Agrippa the Second were both children of king Agrippa the Great (and according to Josephus: children of Salome; their sister was Drusilla—JW I,28,1), but that didn't prevent them from being together.
That is, after Bernice's first husband, her uncle Herod, had passed away. She left brother Agrippa and married king Polemo of Cilicia, but their marriage didn't last long. She returned to brother Agrippa but quickly averted her amorous attentions to emperor-to-be Vespasian, and his son, emperor-to-be Titus, while she was at it.
Whether Bernice ever truly experienced love, the annals don't say.
Etymology of the name Bernice
The name Bernice is a Frenchified version of the Greek name Bernike. The word was also used in the meaning of a throw of the dice, or to indicate a certain plant. The related word Βερενικιδες (berenikides) means (women's) shoes.
The name Ber(e)nice consists of two elements. The latter bit of the name Bernice comes from the familiar Greek noun νικα (nika), meaning victory:
The origin of first part of the name Bernice becomes clear when we realize that the spelling with a beta was the Macedonian form of the more common spelling with a phi: φερενικη (pherenike). Apparently, the b- and the v-sounds were similar enough to allow interchanging. The same happens in Hebrew, that's why we speak of the city called Tell Aviv, which is spelled תל אביב (Tell Abib).
The phere-part of the word pherenike comes from the verb φερο (phero), meaning to bear or carry (a load):
The name Bernice means Bringer Of Victory.