Hortense is the French form of Latin Hortensia — from hortus ("garden"). Hortense de Beauharnais (1783-1837) was the daughter of Joséphine and stepdaughter of Napoleon Bonaparte — who married her to his brother Louis.
Featured in countless Napoleonic histories.
Hortense 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 Hortense reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.