Shizuka (静) is the Japanese word for "quiet" or "calm" — a Zen Buddhist virtue. Shizuka Gozen (1165-1211) was the famous shirabyōshi dancer beloved of Minamoto no Yoshitsune.
Shizuka is widely used in Japan. Shizuka Minamoto is the female lead of Doraemon.
Shizuka 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 Shizuka reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.