"Hello boy, what is your name?"
Translation:Halò a bhalaich, dè an t-ainm a th' ort?
The notes describe the lenition, but not the slenderization, which was what was asked about here.
The examples, however, do show that masculine words slenderize in the vocative (tidsear → a thidseir, ollamh → ollaimh) but feminine ones do not (piuthar → a phiuthar).
For anyone interested in the history, who also knows Latin or Shakespeare, slenderization developed from endings that contained an e or i, and you see this in some Latin words, all masculine (Brutus → et tu, Brute, agus tusa, a Bhrutais, 'and you, Brutus').
It's a bit difficult to say what it is doing. The t was originally part of the article. I cannot remember the exact Old Irish, but in modern Gaelic it would have been
But in Old Irish the spaces were non-existent, or too small to be clear, so, as the t was lost from most situations, people forgot where it belonged and it became
an tainm in Irish
The hyphen was then added for clarity. We always add it when we have a t, h or n stuck on the beginning of the word - these other letters are from mutations that we no longer have.
But in Irish they only use a hyphen when necessary. So if writing a title and using capitals they would write
whereas we would still write
So some grammars actually say that the article in this situation is an t-, which it is really.
Before they put the hyphens in or started using capitals (which they didn't in the Old Irish period) the most confusing example was
Ar nAthair 'Our Father'
Ar Nathair 'Our Snake'
which are still indistinguishable to the ear.