Radio Shack product names not infrequently differed from country to
country, even if only subtly. This answer covers only U.S. naming.
But yes, the TRS-80 Model I was sold new under that name and always
used the Roman numeral. This happened only after the Model II was
released, and the full name including "Model I" was not used
In their U.S. catalogs through 1979, before the introduction of the
Model II, the Model I was always referred to only as the
"TRS-80™ computer." See, for example, the back page and
page 79 of the 1979 catalog, the latter headlined "The
Breakthrough Radio Shack TRS-80™ Computer!"
With the introduction of the Model II, Radio Shack starts using the
term "Model I" sometimes, but not always, and usually only when a
Model II is nearby.
The back page of the 1980 catalog has an inset headlined
"New Low Price on Model I." However, at the computer section of the
catalog starts on page 170 with the Model I but always
called simply the "TRS-80™ Computer" or "TRS-80."
This continues through the next three pages until we get to printers
on page 174, where the page is headlined "Add Printed Output
to Your Model I or II TRS-80." Yet even there the product lines have
things like "Cable for TRS-80 Expansion Interface" listed next to
"Cable for TRS-80 Model II." (Arguably, that's fine because there was
no Expansion Interface for the Model II, only the Model I.)
Even on page 175, where the catalog moves on to the Model
II, the headline is "Meet the TRS-80's Big Brother!" though it
eventually goes on to use "Model I" in the text, mostly:
...whose capabilities begin where the TRS-80 Model I approaches
upper limits. Model II operates at twice Model I's speed, but it's
not intended to replace — or compete with — the original TRS-80.
By 1981 the term "TRS-80" refers to Radio Shack's entire line of
computers, not just the Model III but also the CoCo and the Pocket
Computer (PoCo?), all of which were introduced that year. The
back cover of the 1981 catalog has no reference at all to
the Model I, but displays pictures and descriptions of the "TRS-80
Color Computer,", "TRS-80 Model III" and "TRS-80 Pocket Computer"
under the headline "Radio Shack Introduces a Whole New World of
Affordable TRS-80™ Computer Systems."
The computer section of the catalog starts on page 169 with
a page devoted entirely to the Model I, but the headline "The
Amazingly Expandable TRS-80™." Below this, however, the product
description uses "TRS-80 Model I" (twice). Usage varies throughout the
The next page, page 170, introduces the successor to the
Model I, headlined "The New Model III." The description compares it
with "Model I," and "Model III" is used as a qualifier throughout on
accessories such as disk drives that work only on the Model III.
Page 171 is headlined "TRS-80 Model I & III Software," and
stating that "All programs will work on Model I or Model III unless
otherwise noted." Just a few items have "Mod I only" beside them.
And the rest goes on in that vein.
By 1982 the Model I itself is no longer in the catalog, though there
is a small section of "TRS-80 Model I Accessories" on page
172. The software page still offers "The Growing Library of
TRS-80 Model I & III Software," but "Mod I only" software is gone.