Kind of a tangent on the thread about taking the premise of your next story from a small part of a previous story you've written . . .

What is the convention regarding reusing names? In my newest WIP, I named a major character. Then, while editing my other WIP, I accidentally gave a medium-importance character the same name. Do I need to change one of the names? (I realize I'm being very optimistic that both of them will eventually see the light of day, but one can always hope!) If it helps, the characters are different genders (it's a unisex name) and the name is spelled slightly differently in the two books.

I know Agatha Christie used the name Celia over and over again, but I also know I didn't care for that. I'd love to hear others' personal preferences and any industry conventions I need to be aware of. TIA!