A long time back soundex [1] was used for matching things like names. I imagine there might be yet better algorithms these days but that one probably still solves this problem relatively well.

[1] https://en.wikipedia.org/wiki/Soundex

EDIT: I guess there are better ones: metaphone [2] is a modern improvement on soundex.

[2] https://en.wikipedia.org/wiki/Metaphone

Would this not render fairly unambiguously to MAGUIDHIR (?spelling, corrected in an edit as I got it wildly wrong)? It only seems confusing if you're not Irish, and I'm already completely at sea with names that aren't Western European so this seems like a fine tradeoff to make.

Unambiguously? Yep. (And wow, I'm impressed.)

But you're going to dreadfully confuse people looking for Mark McGwire (https://en.wikipedia.org/wiki/Mark_McGwire), for example. (And possibly "MacGuiver". I'm kind of unconvinced that it's related.)