The Show Aliases Tab
The Show Aliases tab only affects source files, it does not affect show episodes in your media library (TV Rename can work out the correct name for a file in the library from the containing folder structure and the show/season number).
Sources often rename files because of the excessive length of the shows name, for example “Law and Order- Special Victims Unit” could be represented as “L&O-SVU”. Adding “L&O-SVU” as an alias would cause any source file with that abbreviated name be renamed correctly when moved or copied into the library.
Another good example (though for different reasons) would be the BBC1 show “Doctor Who”, The TVDB correctly calls it “Doctor Who” which TV Rename will recognise, however some sources variously call the show “Dr. Who” or “Dr Who” causing some confusion. Adding “Dr. Who” and “Dr Who” as aliases for “Doctor Who” will fix this problem and everything will be correctly named “Doctor Who” when moved or copied into the library.