Aytac is from the Azerbaijani / Turkish Aytaç — ay moon + taç crown — moon-crown, crowned by moon. Aytac is one of the Azerbaijani + Turkish feminine names — central to traditional Azerbaijani-Turkic celestial-naming heritage.
Aytac 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 Aytac reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.