Here are some modern Jain girl names starting with M:

• Maitri — friendship, loving-kindness
• Mokshika — one who seeks liberation
• Mokshada — giver of moksha, liberation
• Manvi — kind-hearted, compassionate
• Madhavi — sweet, graceful
• Mahika — dew, earth
• Minal — precious gem
• Mitali — friendship, bond
• Mridula — soft, gentle
• Mokshita — liberated, freedom-seeking
• Mayuri — peacock; graceful
• Moksha — liberation, spiritual freedom
• Medha — intelligence, wisdom
• Mehulika — rain-like, cool and pure
• Myra — admirable, beloved

If you want, I can also give:

• Jain-inspired modern names starting with M
• Names with meanings related to Ahimsa, peace, or moksha
• Short and unique Jain girl names starting with M