Yhyjyk

(This question addresses the prohibition of referring to your parents by their first name)

Other than emergency situations (medical, hospital etc) are there instances where a child is permitted to refer to their parent by their first name?

For example: my father used to do business with someone named Herb Schuster, who employed a couple of his kids. Now my father called him "Herb"... but so did Herb's kids. Is that allowed?

Furthermore, is this something a parent can mevater, i.e. "I don't mind, you can refer to me by my first name"?

There are instances where a child can use their parent's name.

According to the Radvaz, Hilchos Mamrim 6:3, s.v. אבל, a child may use their parent's name, even in their parent's presence (and presumably even to the parent, although he does not explicate that point), as long as it is qualified with an honorific, such as Reb/Rav Avrohom, or Don Avraham.

R' Akiva Eiger, D'rush V'chiddush Shabbos 115a s.v. אמר ר' יוסי, proves (in the name of his son R' Shlomo Eiger) basically the same thing from a Rashi in Sanhedrin, which says that a heretic is someone who refers to their father as Ploni, and not as Rebbi Mori Ploni (my rebbe my teacher Ploni), which means that with the honorific it would be ok. (Although we see nothing from here about even in the father's presence.)

According to the Maharshal, Yam Shel Shlomo Kiddushin #65, honorifics only work with regard to a teacher's name, but not a parent's name, since you only have one father and there is no need to clarify further than just to say "my father." Pischei Teshuva, Y.D. 240:2 writes that based on this, if someone asked who your father is you could answer with his name, because it's a necessary clarification (but you should still add an honorific).

Regarding if a parent can nullify this, the Gemara in Kiddushin says that a father who pardons his honor, his honor is pardoned. Calling him by name is really a facet of fear, not honor, as the Rambam classifies it, but the Turei Even proves from Kiddushin 32a that even disgracing a parent is in their jurisdiction to pardon.

The Rambam (Hilchos Mamrim 6:8) says:

אֶלָּא יִמְחל וְיִתְעַלֵּם שֶׁהָאָב שֶׁמָּחַל עַל כְּבוֹדוֹ כְּבוֹדוֹ מָחוּל

Rather he should forgive and ignore, as the father that forgave his honor, his honor is forgiven.

So a parent who allows their kid to call them by name, the kid is allowed to call them by name. From the fact that Herb didn’t object to his kids calling him by name, he probably allowed them to call them by name. Nevertheless, it is better to be mechabed, because, as it says in Kiddushin 32b

אפ"ה הידור מיעבד ליה בעו - even so, he should honor him (literally praise him)