I've never seen
Cindy except as a nickname; unlike the Americans who've replied, here in South
Africa I've known a couple of
Cynthia people who just use the full name - no nn - and one
Lucinda who was called
Cindy because she didn't seem like a
Lucy to her family.
That encouraged me to name a cat of mine
Lucinda and call her
Cindy. She "had to have" a name starting with L because she had a pedigree, though we were never going to breed with her, but her face was so naughty that I thought
Cindy would be suitable, because of sounding like Sin! So
Lucinda worked well for her.
For a human, if I wanted a
Cindy I'd certainly use
Lucinda; but if I used
Lucinda I'd shorten it to
Lucy. Except, I'd just use
Lucy as a name in its own right - I find
Lucinda to be dated to the 18th century.