Astghik is from the Armenian Աստղիկ (Astghik — little star, diminutive of astgh star). Astghik is one of the Armenian feminine names — central to traditional pre-Christian Armenian pagan heritage. Notable bearer: Astghik Movsesyan — Armenian-Russian gymnast.
Astghik 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.
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In Pythagorean numerology the letters of Astghik reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.