Here are some girl names starting with H that are popular in Jain and broader Indian contexts, with simple meanings:

• Harini — deer; graceful, charming
• Hemlata — golden creeper; radiant with gold
• Himanshi — full of snow; frosty or snowy beauty
• Harshita — joyful, cheerful
• Hema — gold; precious
• Hiranvi — golden luster
• Hiral — radiant, beam of light
• Himani — snow-covered; sacred snow (also used for beauty)

If you’d like Jain-specific names that reflect virtues (like ahimsa, karuna, or concepts from Jain scriptures), I can suggest those as well.