Anicia is the Latin feminine of the noble Anician family name. Anicia Juliana (462-527) was the Byzantine princess and one of the wealthiest women of the 5th-6th c.
Granddaughter of the Western Roman Emperor Valentinian III.
Anicia 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 Anicia reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.