I worked with a client who asked for a logo design, color palette creation and style guide in exchange for very, very little money. I presented four concepts, each with several iterations. The client chose, the project was completed and files handed off. Does the client have the right to keep the unused logos?? The ones they didn't select turned out to be the best, in my opinion...and given that they low-balled me on project fee, I don't feel that they should get all unused. What if they decide to use them in the future??
Ask yourself a simple question:
What explicit rights are granted (whether by contract or verbal agreement) when you and a client agree to you working on a logo for them?
They expect to pay for thinking / process / production design work, and they expect to pay for a logo or logo family, complete with alternate colour treatments (4-colour, duo tone, b&w, greyscale) all fonts (bespoke or bought w/ all rights) and a range of final output files (raster & vector), and for those final products they expect to have typical use rights for a logoset - any medium, any number of impressions / click throughs / views. They PAY for those use rights.
If they choose also to pay for similar rights to all presented alternative designs... sure, let ‘em have ‘em.
Absent payment explicitly FOR those non-selected designs? Yours as creator, free and clear.
Hope that helps clarify.