Kostis Kourelis has recently posted the third entry (Mapping Eleia) in an interesting series on toponyms, archaeology and GIS. There's no distinctive tag, so I'll explicitly link to the two previous posts as well:
Apropos language, script and transliteration there are many things to consider. It's in this domain of course that the simple, flat-file approach to GIS often breaks down, particularly given the problems of change over time and of fragmentary witnesses. For Pleiades -- which was designed with an object-oriented data model -- we record individual name variants, each of which has a language-and-script combination, an "original script" representation (using Unicode) and a transliteration. We can have as many names assigned to a given "place" as we have variants (or theories).
We have our own slightly idiosyncratic transliteration scheme for classical Greek (inherited from the Barrington Atlas; one of the major benefits of Pleiades is the ability to add back the original orthography). We could easily add multiple transliteration schemes (and the corresponding strings generated programmatically from the Unicode Greek). We may well need such a development when we move, as we eventually must, to include historical toponymy in Arabic (where both past and present variation in transliteration schemes renders even recent bibliography a veritable maze).
If you're trying to do this ArcGIS, you'll probably have to set up a relational database or manage a series of joined tables manually.