Here are some Jain-inspired names with R:

Boys

• Rishabh — first Tirthankar, also means “noble”
• Rajendra — kingly, honorable
• Rutvik — priestly, devotional
• Ratnakar — ocean of jewels
• Rachit — created, well-formed
• Rajat — silver
• Raman — pleasing, delightful
• Rudra — strong, powerful
• Rupesh — lord of beauty
• Riddhesh — lord of prosperity

Girls

• Riddhi — prosperity, growth
• Rachana — creation, composition
• Rujuta — straightforwardness, simplicity
• Ritika — movement, order
• Rajvi — royal, noble
• Rupali — beautiful, graceful
• Rishika — saintly, wise
• Reshmi — silken, soft
• Rasika — refined, tasteful
• Rekha — line, mark

Unisex

• Rayan — path, gate; also used as a modern Jain name
• Ruhani — spiritual
• Ravya — pleasant, respectable

If you want, I can also give:

• modern Jain names with R
• unique Jain names with meaning
• names based on Tirthankars