Here is a list of 100 baby boy names starting with the letter “H” (many are of Sanskrit / Jain usage and are gentle, positive in meaning):

1. Hanish
2. Harshit
3. Harshil
4. Harsh
5. Harshad
6. Hardik
7. Harin
8. Harit
9. Harendra
10. Harendrajit
11. Hareram
12. Harshvardhan
13. Harshwardhan
14. Haren
15. Harinandan
16. Harikesh
17. Hariraj
18. Harjeet
19. Harshul
20. Harikant

1. Hitesh
2. Hital
3. Hitansh
4. Hitendra
5. Hiten
6. Hitanshu
7. Hitanshraj
8. Hitay
9. Hiteshkumar
10. Hitom

1. Hemant
2. Hemanshu
3. Hemendra
4. Hemesh
5. Hemil
6. Hemu
7. Hemraj
8. Hemank
9. Hemarth
10. Hemprakash

1. Haribhadra
2. Hemchandra
3. Harichandra
4. Harigopal
5. Harikrishna
6. Harimohan
7. Hariprasad
8. Harish
9. Haripriya (unisex in some traditions, but can be used for boys)
10. Haridutt

1. Harsiddh
2. Harshdeep
3. Harshilraj
4. Harshank
5. Harshik
6. Harshesh
7. Harshvin
8. Harshendra
9. Harshayan
10. Harshnit

1. Hiran
2. Hiralal
3. Hiren
4. Hiral
5. Hiralbhai
6. Hirak
7. Hiteshwar
8. Hridansh
9. Hriday
10. Hridayesh

1. Hriyan
2. Hrishabh
3. Hrishik
4. Hrishikesh
5. Hrutesh
6. Hrutvik
7. Hridayraj
8. Hridit
9. Hrehaan
10. Hriman

1. Harvijay
2. Harvindra
3. Harvansh
4. Harivansh
5. Harshansh
6. Harayan
7. Harijit
8. Haridev
9. Harinath
10. Harimurti

1. Harirajesh
2. Harishchandra
3. Hemvijay
4. Hemvansh
5. Hemvir
6. Hemtej
7. Hemnath
8. Hemsagar
9. Hemdev
10. Hemrajit

You can choose the one that sounds good with your surname and, if you wish, I can help you with meanings for a smaller set of names you like from this list.