Here are several girl names starting with the letter H you might like:

• Harmila
• Harini
• Harita
• Hema
• Hemani
• Hemlata
• Hansa
• Hansika
• Harshita
• Heera
• Heena
• Hiranya

If you’d like, I can share meanings for any of these or tailor the list to a particular region or language.