As much as I can relate to consistency with HTML (see another suggestion), I believe it (or its formal specification) should not be favored over other output formats.
The (cumbersome IMO) HTML terminology was intended as a breakaway from the <i> and <b> legacy, which CommonMark needs not be concerned with. Emphasis and strong emphasis, on the other hand, have been around for nearly twelve years, and replacing them should not be taken lightly.
However, if consistency with HTML5 terminology is deemed necessary, I’d reluctantly prefer emphatic stress over stress emphasis, as readers familiar with the current terms could easily confuse the latter with the visually similar strong emphasis.