Veena is from the Sanskrit vīṇā — the sacred stringed instrument of Indian classical music. Veena Gowda — modern Indian feminist lawyer. Veena Malik (born 1984) — Pakistani actress. Veena Sopory — Indian classical musician.
Veena 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 Veena reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.