I'd like to add that Radio Times, for week 20-26 February 2016, has published the Emmerdale cast list as to include "Liv Flaherty" and "Sandra Flaherty".

I also just checked the on-screen credits for ITV's Thursday Emmerdale 2nd episode and the spellings there are "Flaherty" too!

So is it Flaherty or Flahery? Time will tell! How odd for this spello to persist for so long!