Indian Names for Baby Girls starting with letter R 

        Rachna          ....  construction, arrangement 
        Radha           ....  Lord Krishna's lover, also means prosperity, nature
        Radhika         ....  Radha, lover of Lord Krishna
        Rajani          ....  night
        Rajanigandha    ....  scented flower
        Rajashri        ....  king's pride, ornament
        Rajasi          ....  worthy of a king, Goddesss Durga
        Rajata          ....  silver
        Rajeshwari      ....  queen ( main ), Goddess Parvati
        Rajkumari       ....  princess
        Rajnandini      ....  princess
        Rakhi, rakhee  ....  thread used in brother-sister bonding during festival of rakhsha bandhan
        Ramani          ....  a beautiful girl
        Ramita          ....  pleasing
        Rambha          ....  name of an apsara
        Rameshwari      ....  Goddess Parvati
        Rangana         ....  happy
        Rani            ....  queen
        Ranjana         ....  entertainment
        Ranjita         ....  amusing, decorated
        Rashmi          ....  a ray of light
        Rasika          ....  sugarcane juice, connoiseur
        Ratanjali       ....  red sandal wood
        Rati            ....  wife of cupid ( Kamdev )
        Ratna           ....  gem
        Ratnajyoti      ....  light from a jewel
        Ratnalekha      ....  beauty of jewels
        Ratnangi        ....  whole body adorned with jewels
        Ratnaprabha     ....  Earth, light from a jewel
        Ratnapriya      ....  one who likes jewels
        Ratnamala       ....  jewels necklace
        Ratnavali       ....  a bunch of gems, Earth
        Rekha           ....  line
        Renu            ....  molecule, particle, Earth
        Renuka          ....  molecule, Earth,  Parshuram's mother
        Reshma          ....  soft  &  shining like silk
        Reva            ....  Goddess Durga, Narmada river
        Revati          ....  wife of Balarama, 27th nakshatra
        Ritika          ....  bronze
        Roma            ....  Goddess Lakshmi
        Rohini          ....  4th nakshatra, cow, lightening
        Roshni          ....  light
        Roshan          ....  bright
        Ruchi           ....  taste
        Ruchira         ....  saffron, tasty
        Ruchita         ....  beauty
        Rudrabhiravi    ....  Goddess Durga
        Rudrakali       ....  Godess Durga
        Rudrani         ....  a wife of Shiva (iDurga), a raagini
        Rudrapriya      ....  beloved of Rudra (Parvati/Durga)
        Rukma           ....  golden
        Rukmini         ....  wife of Krishna
        Rupa            ....  beauty, silver
        Rupali         ....  beautiful, pretty
        Rupashri        ....  a musical raagini
        Rupasi          ....  beautiful lady
        Rupi            ....  beauty
        Rujul           ....  soft spoken
        Rujula          ....  who endows wealth, Goddess Lakshmi, soft, innocent
        Rujuta          ....  honesty, sincerity
        Raima          ...... Pleasing; Rama of the axe    ( origin - Sanskrit : Root: Rama)