Ibtisam is from the Arabic ابتسام (Ibtisām — smile, smiling) — from Arabic basama (to smile). Ibtisam is one of the Arabic feminine names — central to traditional Arab heritage.
Ibtisam 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 Ibtisam reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.