Here are some baby girl name ideas starting with H, commonly used and liked in Jain families (with simple meanings):

1. Harshita – खुश / प्रसन्न, always happy
2. Hema – सोना, golden, precious
3. Hemali – स्वर्ण जैसी, one who shines like gold
4. Hiral – हीरे जैसी, full of brightness / wealth (in virtues too)
5. Heena / Hina – सुगंध, fragrance
6. Himani – हिम से बनी, pure like snow
7. Hita – हितकारी, well‑wisher, one who does good
8. Hitanshi – सबका हित चाहने वाली, one who wishes good for all
9. Hrida / Hridi – हृदय से जुड़ी, pure-hearted
10. Hrishika – इन्द्रिय / रस से जुड़ी, one who enjoys noble things
11. Hrudaya / Hridaya – हृदय, kind‑hearted
12. Hansa / Hansika – हंस, symbol of purity & wisdom
13. Hemansi – स्वर्ण सी पवित्र आत्मा, golden (pure) soul
14. Hemisha – धरती की देवी, goddess of the earth
15. Harini – हरिणी, gentle like a deer
16. Hansini – हंस जैसी, pure and graceful
17. Harsika – आनंद से भरी, full of joy
18. Hitarthi – हित + आरती, one who prays for well‑being of all
19. Himadri – हिमालय, strong and steady like a mountain
20. Hemlata – स्वर्ण लता, golden creeper (symbol of growth & grace)

If you tell me:

• your gotra,
• any preferred starting syllable (like “Hi”, “Ha”, “He”),
• and if you want a purely Jain/granth-based type meaning (like connected to virtues: अहिंसा, क्षमा, दया),

I can suggest a more focused short list for you.