Imagine your parent changes his or her (Hebrew) name--either by converting to Judaism and getting a name, by taking on a second name, or simply changing his/her name for whatever reason. (Not sure that the latter is often done...)
In this case, does your Hebrew name also change? Do you need to go through the procedure for reifying a name change?
(1) If you were Ploiny ben Yitzchak and your father becomes Yitzchak Chaim, do you become Ploiny ben Yitzchak Chaim... at all? automatically? after officializing it?
(2) If you were Ploiny ben Patrick and your father becomes Pinchas Reuven, do you become Ploiny ben Pinchas Reuven...at all? automatically? after officializing it?
~~~ BONUS: What if your mother changes her name? Does your name for prayer also change?