Here are some good baby boy names starting with H, commonly used in Jain families, with simple meanings:

1. Hardik – From the heart, sincere, heartfelt
2. Harsh – Happiness, joy
3. Harshit / Harshil – One who is happy, joyful
4. Het – Love, affection
5. Hetan / Hetul – Full of love, joyful
6. Hitarth – Good purpose, for others’ welfare
7. Hitesh – Well‑wisher, friend of all
8. Hemal – Golden, full of brightness
9. Hemanshu / Hemansh – Part of the moon; cool, calm nature
10. Hemant – A pleasant season; cool, calm
11. Hemendra – Golden lord, noble and bright
12. Hemchandra – Golden moon; name of a great Jain acharya
13. Himanshu – Moon; one who spreads coolness and peace
14. Hriday / Hridyansh – Heart; kind‑hearted
15. Hrishabh / Hrisabh – Righteous, exalted (related to Ṛṣabh – first Tirthankar’s name form)

All these names are ahimsak, positive and perfectly suitable in Jain culture.

You can also see a broader A–Z Jain boy name discussion here