What's the most appropriate name for non-italicized text: "roman" or "upright"?

Once again I turn to The Chicago Manual of Style, 14th Edition, which states

2.83: [...] To change words typeset in an italic typeface, underline or circle the words and write "rom" or "roman" in the margin. For longer underlined passages that are to be set in roman type (not italicized), circle the text involved and write a note to the typesetter in the margin:
  (set roman)   [parentheses here indicates that text is circled]

Speaking as someone who has done a little bit of proofreading work, using the word "roman" (in lowercase) in this context will not be confusing to anyone on the receiving end of the proofing notes.

I don't work as an editor, so there may be standard terminology for this, but as an English speaker, I would say that the clearest thing to write is "please don't italicize this".

The technical name for non-italic fonts is roman or romanized, so this is probably your best choice from the options you've given. I would avoid calling it upright.

In typography terminology, roman (or normal) is the antonym of italic, while upright is the antonym of oblique (aka slanted). Oblique type and italic type are not the same, as the Wikepedia article 'Oblique type' explains and illustrates. Some typefaces have separate italic and oblique fonts. No typeface (AFAIK) has separate roman and upright fonts, so the choice between these words depends on which of italic or upright you wish to draw a contrast with. So if the author has inappropriately used an italic font rather than a slanted font, 'please typeset in roman' would strictly be more appropriate than 'please typeset upright'. But the typesetter will set the same type whichever you use.