If your parent changes their name, does your name change too?

Question

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?

That is:

(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?

Answer 1

I found a reference that once the name has been changed, the children are to use the new name from that point on. They are called to the torah with the new name and do not have to undergo any procedure.

The Halacha of Changing One’s Jewish Name Summary provided by Rabbi Levi Alter

The Sefer Ta’amei HaMinhagim quotes from the Shaloh Kitzur 335, Inyanei Sefer Torah that this name will be used when the person and person’s children are called to the Torah. In the Shulchan Aruch Even HaEzer Siman 129 Sif 18 the Ramo rules regarding a Get that the new name and any nickname associated with it is to be mentioned first. The Pischei Teshuvah Sif Katan 53, 54 and the Be’er Heitev Sif Katan 32 concur.