What is the original name for a TARDIS?

Question

It is my understanding that the acronym "TARDIS" was coined very early on in Doctor Who by the Doctor's granddaughter, Susan, giving a name to the wondrous vessel they travel in.

These vehicles were common amongst Time Lords, so my question is why was the name coined only then rather than there being a pre-existing name for these vehicles?

Furthermore, how does the name catch on with other Time Lords and other species aware of these vehicles? For a human comparison, wouldn't it be similar to giving your own car a nickname while everyone else would still refer to it as a "car"? If your granddaughter called your car "TARDIS" other people would still refer to it as a "car", it's original universally recognised name, rather than whatever you or your family call it.

Answer 1

From the thedoctorwhowebsite.co.uk page for the TARDIS origins, we see that the vehicle is known as Type 40 Mark | TT Capsule where TT stood for Time travel. It's likely this (or TT Capsule) was its name before TARDIS.
The link goes on to say that it is possible it had been named the TARDIS before.

However it was later suggested that this was a common name used by all Time Lords to describe the machines.

With regards to your second point, this related question has a possible answer to that, although it has no accepted answers, in short it talks about how (in-universe) different species calling it a TARDIS is likely only due to the translation from the original language's name for the TT Capsule into English, whereas out of universe it's likely jus a simplicity thing. Known by TV Tropes as the "Translation Convention" (WARNING: TV Tropes link!)

Answer 2

There are 2 words "Tardis" in Dr. Who. The word "Tardis" that is actually spoken and the word "tardis" that is a sort of translation into English of one or more words in one or more alien languages.

Susan may have named the tardis the T.A.R.D.I.S. (Time and Relative Dimension In Space) after learning the English language some time before the events of "An Unearthly Child".

Since the tardis translates alien words into English language thoughts for the English speaking companions of the Doctor, it may have decided to translate very vague or specific, short or long, Gaillifrian versions of a "Type 40 Mark | TT Capsule" as "tardis" for the benefit of Ian and Barbara, and for the next companion they picked up, and kept it up for all the succeeding companions. There were only a few times in classic Dr. Who when a new companion was introduced without the Doctor already having one or more companions used to calling the tardis a tardis.

Thus the "tardis" heard in episodes may sometimes actually be spoken as "Tardis" and may sometimes actually spoken as alien language phrases such as "xi dosh" or "Grang Strup Mon" or "Salyfel", or whatever, used to describe Time Lord time machines.