We would probably say:
'Dia Dhuit, conas atá tú? Is Mise Jenny!'
Phonerically, something like this:
Deeya Gwith, kunnas a taw too? Iss Misha Jenny
Translates as: 'God be with you, how are you? I am Jenny'. It's fairly literal that one.
You could say : 'Tá athas orm buileadh leat' to say 'it's nice to meet you' but to my memory, it's not a common greeting. Phonetically, that would sound like
'Taw aw-has urum bool'eh lat' and the literal translation is more like 'I have pleasure meeting you'