Where did the name "T-800" come from?

Question

After watching The Terminator and Terminator 2, I can't find any reference to Schwarzenegger's Terminator being called the "T-800". Yet I distinctly remember in promotional material, computer games, etc. at the time, he was called the "T-800". (He refers to himself as a "Cyberdyne Systems Model 101" at one point)

So my question is, where is it mentioned that he's called the "T-800"? Please limit the answers to the first two movies - while this name/sku may be mentioned from the third movie onwards, he was definitely being called the "T-800" by sources (out-of-universe) before then.

Answer 1

There is a deleted scene included in the "Skynet Edition" Director's Cut of Terminator 2 in which The Terminator sees himself in a mirror while he runs a diagnostic. Whilst doing so, you can see he is a Cyberdyne Systems Series 800 Model 101 Version 2.4 Terminator.

Additionally, there is an omitted scene that was removed from the movie entirely where Sarah, John and Arnie end up at the ranch of one Travis Gant. There is some dialogue between Sarah and Gant as she tries to persuade him to help, then:

SARAH: Tell him what you are.

TERMINATOR: Series 800 terminator. Model 101. Cyborg tactical infiltrator.

Again identifying him as a Series 800 Model 101.

Answer 2

The Series 800 name is mentioned twice in the script for Terminator 2: Judgement Day:

TILT UP, revealing a humanoid machine holding a massive battle rifle. It looks like a CHROME SKELETON... a high-tech Death figure. It is the endoskeleton of a Series 800 terminator. Its glowing red eyes compassionlessly sweep the dead terrain, hunting.

...

We realize now that the cop is a terminator too. We don't know the details yet, but let's call him the T-1000 (since that's what he is). A newer model than the one we've come to know so well (the 800 Series "Arnold"). This guy's a prototype... and he's got quite a few surprises.

Additionally, the Terminator Wiki's article on the T-800 mentions in the references that the HUD identifies it as a Series 800 in Terminator 2 (I'm not sure if this is only in the deleted scene mentioned in @DisturbedNeo's answer or if it also appears in another scene as well). The references also note that James Cameron referred to both the Series 800 and 1000 Terminators in the Terminator 2 commentary. (The commentary is not available to me at this time so I can't confirm.)

The Terminator Wiki's article on the Model 101 also has a screenshot from the Terminator 2 teaser trailer showing the Series 800 designation:

Note that "Model 101" refers to the human appearance of the Terminator (Arnold Schwarzenegger) rather than the model (series) of the endoskeleton. Other models have different appearances, such as the Future Terminator (Model 102) portrayed by Franco Columbu.