T-V distinction

In many languages, there is such thing as T-V distinction. Basically, it's when you use different pronouns in "formal" (or "polite") speech, and in informal speech.

Now, I do realize there is no such thing in English directly. However, there are phrases that indicate the change between the formal and informal pronoun. For example, in Russian, a phrase "перейти на 'ты'" means literally "to start using 'ты'", where 'ты' is the informal pronoun. Variations of this also exist in other languages.

So my question is, what is the best way to translate such a phrase into English? In Poul Andersen's book "Tau Zero", I've found a phrase

“That’s the main reason I called you. Remember, during training I urged you to come here for part of your furlough.” By now they were using the intimate pronoun.

While this seems a little awkward, it does the job well. Are there any other ways of saying it?

We might say "By now they were speaking more familiarly" or, in slightly different contexts, "By now they were on a first name basis"

I tried to find a similar phrase in German so I could translate it and all I came up with is "Du Sagen" "To say 'informal you'".

English does have something of a T-V distinction, but it occurs in a different way than via a pronoun switch.

In the formal version, one peppers one’s speech with vocative-style sir and ma’am all over the place, and addresses the other party by title and surname, like Mr Smith.

In the informal version, one drops all the sir/ma’am bits, and addresses the other party by their given name instead.

This clear distinction in how to address the other party happens even when the rest of the speech is comparatively high register or low register.

French has tutoyer. There is no equivalent English word, and you just have to get round it by saying something like 'they were now on more intimate terms, and it showed in the familiar forms of address they used with each other.'