Bella(to Edward) in BD part 1: "I was playing around with our moms names,Renee and Esme,and I was thinking Renesmee.Even though Esme is not his biological mom,he considers her his mom.
Bella says she was playing with their moms name Renee and Esme so she thought of the name Renesmee and of course the second name of Renesmee which is Carlie is from their father's name Carlisle and Charlie:)
The name Renesmee came from the names Renee (mother to Bella) and Esme(mother-in-law to Bella),
Her Middle name Carlie came from Carlisle( father-in-law to Bella) and Charlie(father to Bella)