Arsinoë (Ἀρσινόη) is from the Greek arsis (lifting up) + noos (mind). The name of seven Ptolemaic queens of Egypt — most famous Arsinoë II Philadelphus (c. 316-270 BCE), who married her own brother Ptolemy II Philadelphus, was deified during her lifetime as Thea Philadelphos ("Sibling-Loving Goddess"), and became the most powerful woman in the Hellenistic world. Arsinoë IV (c. 68-41 BCE) was Cleopatra VII's younger sister — exiled to Ephesus by Caesar, executed there by Mark Antony at Cleopatra's request — among the most notorious sibling rivalries of antiquity.
Subject of Grace Macurdy's Hellenistic Queens (1932).
Arsinoe 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 Arsinoe reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.