Here are some common Hindu/Jain-era boy names starting with H, with brief meanings:

• Harsh — joy, happiness
• Hemant — early winter; also a precious metal with shine
• Hitesh — one who thinks well, lord of success
• Hrishikesh — lord of the senses; one who is controlling his senses
• Harendra — king of hearts, ruler of hearts
• Hetu — cause, reason
• Hiteshwar — lord of auspiciousness
• Hriday — heart

If you’d like, I can tailor suggestions to a preferred meaning or style (classic, modern, or tradition-focused).