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If I do:

ListPlot[Range[10]
,PlotLegends->Placed[LineLegend[{"Subscript[N, σ] f(m; μ, p)"},LabelStyle->{FontFamily->"Times"}],{0.8,0.35}]
]

where instead of the Subscript parts I've used the Insert -> Typesetting -> Subscript menu option from the front end, I get the following plot:

enter image description here

Why is the N italicized while the f, m, p are not? What can I do to make the N appear upright?

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To fix this, you could create a FormBox wrapper before typing the legend, by using Cell > Convert to.. > TraditionalForm. A quick way to do this is to start typing a single letter, highlighting it and then invoking the conversion. From there on, you can continue typing the label and there won't be any visible difference until you evaluate the cell to create the plot. Then the TraditionalForm wrapper will insure that the default for single-letter symbols is italics.

Here is a movie showing how I typed this:

typingInstructions

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