I did a little searching online, since I'm curious now. I know that no one in the 'scene' called punk 'hard core' or 'hardcore' punk back in the day. But I wanted to be sure.
I see a couple references using Google Books. In 1978, I found a reference in the Los Angeles Times to
"Bands, too, have begun running for cover. Many of the aggresive, hard-core punk units have adopted new battle slogans - power pop or new wave - and softened their stance. Punk is now a commercial liability. No one wants to be associated with it. Except the Clash.
"We're a punk rock band," boasts the Clash's Mick Jones. "We're true to the spirit of '76 (in England). When other bands saw what was happening, they thought punk was going to be the next 'big thing.' So they wanted in.
"Most of them were crap. They were just trying to cash in on what a few good people had started. But then the Pistols came over here and kinda flunked, so the rush to punk has skidded to a stop. The bands are rushing off somewhere else. Good riddance. We'll carry on. In a year, those other bands will be crawling back."''
In the above reference, although the LA Times uses the term, they seem to be using it as a descriptor, not as a name. Like saying I am a 'hard-core' IT worker. There is no designation for that, it's just a modifier. The use the term 'punk rock' repeatedly throughout the article, and do not use the term 'hard-core' again.
In 1981, Rolling Stone Magazine used the term thusly:
"But instead of coming up with a mere handful of Nuggets, both Echo and the Bunnymen and the Teardrop Explodes strike solid rock by applying recent history — hard-core punk bash, the harmonic tangents of Public Image Ltd. and Joy Division, electronic pop Ć la Ultravox — to the sounds of yesteryear."
Once again, the term seems to be used as a modifier, not a label. And frankly, Echo and the Bunnymen, punk? NO.
Billboard Magazine used the term once in 1982, referring to the Bad Brains as a "Hard-core punk band from Washington, DC..." This is the first time I see the term used as a label, something that says it is a 'thing'. And for all I know, Bad Brains could have referred to themselves that way - they were not a SoCal band, so I never saw them or heard much about them.
Cincinnati Magazine used the term in 1983, but they used it to refer to how college students were dressing, saying that "they don't go in for the hard-core punk look, that is, leather, chains, and studs." So to them, apparently, 'hard-core' punk was a fashion trend that they didn't care for (their students, they said, were wearing madras prints).
Now, by 1984, the term was starting to pop up in various places, clearly referring to a genre. Bands mentioned? Metal Moo Cow, Cottage Cheese from the Lips of Death, a compilation CD called "Rat Music for Rat People," The Dead Kennedys, Throbbing Gristle, and independent record label "Savoy Records."
One reference I found was in Billboard from 1980, referring to an album I have and bands I listen to, Rodney on the ROQ Vol 1, referring to the music as "hardcore punk sounds," but classifying it under 'Pop Music'. So I'm not sure what to make of that.
On the whole, if I had to venture a guess, it would be that the term 'hardcore' or 'hard-core' was a way to differentiate various types of sounds bands that were calling themselves 'punk' were making; applied first as a descriptor and only LATER as a label. It's kind of like the Marines of WWI being known as the "Old Breed." They certainly were not called that at the time. That came later and was a label applied by others.
If one wants to refer to what was punk at the time I was going to the shows as 'hard core' punk, I guess I get it now; but I can assure you that neither I nor anyone I knew was calling it that at the time. We called it punk and that is all we called it. That someone else came up with a name for it later doesn't change what it was then.