I've noticed we have some (a minority) of Chevrolet Silverado HD models listed as the model name 'Silverado HD', while a majority of others have 'HD', '2500HD', '3500/3500HD', etc. in the extra info section. Should I put them all as model name Silverado with the 'HD' in extra info, or should I go through and change the model name on the others to 'Silverado HD' and 'Sierra HD' bring them more in line with how the Ford and Ram pickups are listed (F-150 vs. F-Series Super Duty/Ram 1500 vs. Ram Heavy Duty)?

I know there was a discussion about this a few years ago, but I don't remember what conclusion was reached, if any.

I don't know how important is that mention.
I'd say that it can go as extra info, but if it is an important distinction in the model it is not a problem to have it in the name.

I would say it's fairly important, as the HD trucks have an entirely different chassis and the codes to go along with it. For instance, we list Sierra Denali as a model name, which is not nearly as important as the distinction between a light-duty (1500) and heavy-duty (HD) model.

I haven't looked into it but did Chevrolet market them as a separate model, like Ford and Ram do? And when did they start doing that?

Yes.

2001 was when the Silverado HD and Sierra HD were formally introduced.

The only one that's iffy is the 2001-2003/2005-2007 1500HD (was dropped for '04 and brought back in '05). Sometimes it's in the brochure with the light-duty 1500 trucks, other times it's marketed with its bigger brothers.

Television commercials for the Silverado HD:
https://www.youtube.com/watch?v=JoZy1lY0n4E
https://www.youtube.com/watch?v=-yDOg7wUJ5k
https://www.youtube.com/watch?v=88DKWIlj01M

Brochures:
'03: https://www.motorologist.com/wp-content/uploads/2003-Chevrolet-Silverado-HD-brochure.pdf
'04: https://www.xr793.com/wp-content/uploads/2021/11/2004-Chevrolet-Silverado-HD-Spec-Sheet.pdf
'11: https://www.auto-brochures.com/makes/Chevrolet/Silverado/Chevrolet_US%20SilveradoHD_2011.pdf
'15: https://cdn.dealereprocess.org/cdn/brochures/chevrolet/2015-silverado2500hd.pdf
'22: https://www.chevrolet.com/content/dam/chevrolet/na/us/english/index/shopping-tools/download-catalog/08-pdf/2022-chevrolet-silverado-hd-ebrochure.pdf