Back to the original topic, one could reasonably argue that the TOS-era Enterprise has but one transporter room, since it's often called "the" transporter room, or just "Transporter Room" with no additional distinction.
As far as I can tell, it's not just "often" but always
referred to as if it were unique. I searched all scripts looking for a hint of more than one, but didn't find it. So canonically speaking, there seems to be only one.
But that will never do. Common sense, and the variety of implied corridor configuations in various episodes, will want us to want more than that. Based on the on-screen dialog, maybe the "fudge factor" is that that perhaps there is a "main" or "primary" transporter room and then some additional ones, but they omit saying "main" for convenience and it's understood that the lack of a disambiguator means the primary one — just as I assume there's more than one sickbay, but when somebody says "sickbay" or "the sickbay" it means the primary one.
However, I would expect that walk-and-talk scenes in various episodes will probably poke holes in this stretch; probably we've seen "the" transporter room implied to be in the primary hull at some times, and the second hull at other times. (Not to mention that building a separable starship without beaming capability in both hulls would be just plain idiotic.)
So, maybe when you say "the" transporter room, it means the primary transporter room in whichever hull makes contextual sense
. If you mean any other one, then you have to say "transporter room 3" for clarity. But of course this requires one TR in each hull to be somehow more "special" than the others, just as I assume that the primary sickbay is the one that has McCoy's office and the lab directly adjacent to it.