Renraku has their Red Samurai, Aztech has their Jaguar Warriors. In my current campaign, Wuxing is a major opponent, so I invented an iconic HTR unit for them - I called them the "Tianlong", or "heavenly dragon".

What other megacorps have cool HTR, canonically or just stuff you made up?

Ares has Firewatch. Ares also has Knight-Errant and HardCorps, depending on what they intend to do.

Lone Star has their S.W.A.T. and FRT teams.

Horizon has the Dawkins group. Not quite the prototypical HTR unit, but HTR nonetheless. I think.

The Atlantean Foundation has their Templars.

I have a made up AA corp called Magical Sciences Research Labs Inc. (MSRL). I called their HTR team the Nephilim.

Eh, it worked for the time. I would probably keep the name because I am lazy like that...