Here are some Jain-inspired baby girl names starting with H:

1. Harini — gentle, graceful
2. Hemali — golden, pure
3. Hita — beneficial, auspicious
4. Hiral — jewel-like, precious
5. Hetal — friendly, loving
6. Himani — pure, snowy, serene
7. Harsha — joy, happiness
8. Hridya — loving, from the heart
9. Hina — soft, graceful
10. Hansika — like a swan, pure and elegant

If you want, I can also give you:

• more Jain baby girl names with H
• names based on meaning
• modern + traditional Jain names