Taina is from the Tupi-Guarani Tainá — star (sometimes interpreted pure / fresh). Tainá is one of the Tupi-Guarani feminine names — central to traditional Brazilian Indigenous heritage. Brazilian feminine name reflecting Amazonian Tupi-Guarani heritage.
Taina 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 Taina reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.