Bernice (Βερενίκη) combines the Greek pherō (to bring) and nikē (victory) — meaning "bringer of victory." In the New Testament, Bernice is the sister of King Agrippa II before whom Paul testified (Acts 25:13).
Bernice peaked at #76 in the U.S. in 1925. The Bernice asteroid (number 8002) was named for the queen. Bernice Pauahi Bishop (1831-1884) was the Hawaiian princess and namesake of Bishop Museum.
Bernice does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Bernice reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.