Concha

Only use this name if you're in Spain. «Concha» means something completely different in other countries. In Mexico, it's a kind of food, and in South America, it's a female body part.

I don't know how Concha can derive from Concepcion. Anyway, while it is overly common in Spain, women named Concha or Conchita are likely to be teased in Latin America, for in most countries Concha means, well, that part of the female anatomy, between your thighs.