Yet another tag that was given new meaning in HTML5, <small> apparently lives on:
http://www.w3.org/TR/html-markup/small.html#small
The small element represents so-called “fine print” or “small print”,
such as legal disclaimers and caveats.
This unofficial reference seems to take it a little further:
http://html5doctor.com/small-hr-element/
<small>is now for side comments, which are the inline equivalent of
<aside>— content which is not the main focus of the page. A common
example is inline legalese, such as a copyright statement in a page
footer, a disclaimer, or licensing information. It can also be used
for attribution.
I have a list of people I want to display, which includes their real name and nickname. The nickname is sort of an “aside”, and I want to style it with lighter text:
<li>Laurence Tureaud <small>(Mr.T)</small></li>

I’ll need to do something like this for several sections of the site (people, products, locations), so I’m trying to develop a sensible standard. I know I can use <span class="quiet"> or something like that, but I’m trying to avoid arbitrary class names and use the correct HTML element (if there is one).
Is <small> appropriate for this, or is there another element or markup structure that would be appropriate?
The spec you’re looking at is old, you should look at the HTML5 spec:
https://html.spec.whatwg.org/multipage/
I suggest
<em>here instead of small:<small>is not used commonly in an article sentence, but like this:Article sentence: