I didn’t understand what you mean. If the listener wouldn’t say “Blessed is He and blessed is His name,” but after hearing the name of the Lord he would say, “the Merciful and Gracious One, etc.” — that also wouldn’t be considered an interruption because it is “part of the matter of the blessing”?

If that became part of the accepted protocol of the blessing (which is a two-sided ritual), then why not? Right now, in some places, “Blessed is He and blessed is His name” is part of the broader blessing framework, while “the Merciful and Gracious One” is not.

In principle yes, but simply speaking, the Proposer is right.

You can’t insert “protocol” into the wording of a blessing; the wording was established by the Sages, and any addition is an interruption. The Rosh, who said “Blessed is He and blessed is His name,” did not presume to establish this as “protocol”; he said it only in a case where there was no problem of interruption.

I didn’t insert it into the wording of the blessing. It is not part of the wording of the blessing, and still there is no interruption here.
You are assuming that anything that is not part of the wording is an interruption. But that is not necessary. For example, between washing the hands and saying “who brings forth bread,” it is permitted to ask for the salt and the like. Something connected to the matter does not interrupt. Even regarding a physical barrier, they say that anything that serves to beautify it is not considered an interposition. Here it is definitely similar to beautification.

Either it is part of the wording of the blessing or it is necessary for the blessing (as Rashi says on Berakhot 39b: “This speech is for the need of the blessing, and therefore is not an interruption.” And similarly in Tosafot, that only speech needed for the commandment over which one is reciting the blessing is allowed). “Blessed is He and blessed is His name” is not needed for the blessing; it is just general praise to the Holy One, blessed be He, that people have the custom to say during a blessing.

Sagi, I already wrote that even beautification is not considered an interposition. Need is only one of the criteria for what does not interrupt.
I’ll give another example. What used to annoy me was that in minyanim of kollel fellows in Bnei Brak, they had the practice of silencing singing during Hallel when they repeated the text more than once, and the extra-scrupulous would not even agree to allow one repetition, on the grounds that it is an interruption from the blessing. In my opinion there is no interruption there at all, since the singing beautifies the recitation of Hallel. That is the way to say it. Here too, the repetition is not the formal text of Hallel, and not even something needed for Hallel.

You are drawing an analogy from physical interposition to interruption in blessings, which does not seem reasonable to me. A minority portion does not constitute an interposition for immersion, so shall we say that a minority amount in a blessing also would not count as an interruption?! Now, I’m not saying this reasoning is impossible; it is possible, and of course it has already been said, but I don’t see any necessity to say it, and the burden of proof is on the one making the novel claim.

* By “a minority amount in a blessing” I meant: would we say that one word would not count as an interruption because it is only a minority amount?! Obviously we do not say that, even though regarding a “physical interposition,” a minority does not interpose. So clearly the definitions are different, and therefore one cannot learn from the rule that things which beautify the vessel are not considered an interposition, that in a blessing “beautifying the blessing” would also not count as an interruption.

First of all, a minority portion that one is particular about does constitute an interposition (at least rabbinically. And as is well known, blessings are rabbinic). Beyond that, I made this argument as a possibility (“this is not necessarily an interruption”), and your whole argument was that it is not possible. If now you agree that it is possible though not necessary, then we are back to my original claim. I say that too.

There are the Meiri and the Rashba, who write that if one recites over water, “Blessed are You, Lord our God, King of the universe, who creates the fruit of the vine, by whose word all things came to be,” this is not an interruption, because that too is praise connected to the matter of the blessing.
Because the point of the blessing is to praise God, saying “who creates the fruit of the vine” is no worse, since even if a person is not drinking wine, it is still true praise.
The Rosh writes in the name of his father, “Each and every blessing, in every place…” and did not distinguish between blessings through which one fulfills his obligation and blessings through which one does not… The Tur and the Shulchan Arukh copied this. And so too the Rokeach wrote a hundred years earlier that this is the universal custom.

And Rabbi Zini wrote an article about the liturgical poems inserted into the prayer service and into the blessings of the Amidah and the blessings of the Shema, arguing that according to the overwhelming majority of the Geonim there is no interruption involved (provided a Torah scholar composed them). And in that article he mentioned that he had written an unpublished article about interruption in blessings and about “Blessed is He and blessed is His name” (in response to Rabbi Ovadia’s ruling, which canceled the custom of Jews from North Africa).