what is the name of the fee that would be charged to compensate for work done if the logo was not used?

Answer 1

It would be called a Design Fee. When you create something for profit, it doesn't matter if the other person uses it or not, your services were still used. Unless of course your contract specifies you only get paid if they use it, then you would have contingent contract and would not be entitled to pay.

Answer 2

Creative Fee

Answer 3

If there's no prior agreement, there is no fee.