I would have one caveat to that idea, and that is, if the client had solid evidence that the names provided were essential of the same root derivation, then I might consider no added fee.

I recall a similar incident in the past were two title officers argued about checking the name "sam" for "salvadore" and I settled the matter decisively by informing the party against doing so that my own fathers first name was Salvadore but that he went by Sam. 

Just be sure to always document your research in your notes.  The more complete, the better, should any future questions arise.