Sorry, I could only find two names for today, and was unable to locate any male names in either category. It’s a very uncommon letter in modern Italian names too.
Female names:
Honesta (I) comes from a Latin word meaning “reputable, honourable, respected, distinguished.”
Humiliana (I) comes from the Latin word humilis (humble).
Onomastics Outside the Box 
I found H to be a challenge with my theme as well. My theme is writing words. I was surprised when I struggled with letter H, but in the end the post got written: https://writingiscommunication.wordpress.com/2021/04/09/h-h-writing-words/
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