Padhraic is pronounced "Paw-rick". The letter "d" is silent since combinations of letters like adh act like a vowel sound ("aw" as in "raw") in Gaelic. This is a Gaelic version of the name Patrick which in turn came from the Latin/Roman name Patricius.

Padhraic is a fairly common name in Ireland (but obviously less common in places like California). Somewhat confusingly there are multiple different spellings of the name in Ireland, such as Padraic and Padraig. To further confuse things, the pronounciation is also different in different parts of Ireland - in the very south of the country (like Cork) the name Padhraic might be pronounced something like "Pawd-rick", i.e., the "d" is pronounced and no longer silent. But I'm from the West of Ireland, where "Paw-rick" is the appropriate pronounciation.

There are other idiosyncracies to Irish names. For example although my surname is Smyth (pronounced like the regular "Smith") the Gaelic version of this is Mac Gabhann which is pronounced "Ma-gow-an" (so "abh" acts like the vowel sound "ow", as in "owl"). Translated literally, Mac Gabhann means ``son of the blacksmith" (hence the Smith/Smyth translation into English). My father wasn't a blacksmith, but his father (my grandfather) was: Thomas Smyth of Blanemore, Straide, Co. Mayo. And coincidentally my mother's father (my other grandfather) was also a blacksmith in his village: Dominic Costello, Raherolish, Kilmovee, Co. Mayo.

Many Irish people (such as myself) have the English version of their names on official documents like passports but use their Irish names for everything else (e.g., John/Sean, William/Liam, James/Seamus, and so on). Its a long story, but we tend to blame the English for all this confusion :)