Hmm, My strong preference is for const AFilename: String;
For the reason that especially for larger projects, if you ever need to add source code from another coder, if they have used lots of custom types like TCustomerID, THashValue, TInterestRate, instead of Integer, Cardinal, Double, then you have lots of the above mentioned E2033 to resolve.
Even lots of delphi built in source code doesn't use TFileName, like:
function MatchesMask(const Filename, Mask: string): Boolean;
Furthermore if I have a variable defined like AFileName: TFileName;
then its obvious its a filename & the named type doesn't add any readability for me, if anything in some cases it makes code less readable, because you have to click through to check what actual variable its derived from.