Here are some modern Jain girl names starting with V:

• Vaidahi
• Vaishnavi
• Vamika
• Vanya
• Vedika
• Vihana
• Vritika
• Vanshika
• Varunika
• Vasundhara
• Vasviki
• Vaidehi
• Vidhi
• Vishika
• Vinika
• Varnika
• Vihana
• Vrinda
• Vibha
• Veenika

If you want, I can also give:

• Jain-inspired meanings
• short and unique names
• names from Jain tradition starting with V