HG would be the short form used to represent the name Dødheimsgard, a made-up word conjunction of three words: Død which means death, Heim which means home, and Gard which means (at least in this context) mansion. A natural translation of Dødheimsgard into English would be 'The Mansion of Death', alternatively 'The Realm of the Dead/Death'.
The band released their debut album Kronet Til Konge in 1995. They changed members several times during their career, along with their music, from black metal to some kind of Darkwave/Industrial/Black metal hybrid. In the year 2000 they shortened their name to the present DHG. The band completely changed its line-up in 2002 to the current Bjorn Dencker (a.k.a. Aldrahn; ex-Zyklon-B/ex-Darkthrone/ex-Old Man's Child/ex-Isengard/ex-Thorns/ex-Dimmu Borgir; vocals), Carl-Michael Eide (a.k.a. Aggressor/a.k.a.Czarl; ex-Aura Noir/ex-Dimmu Borgir/ex-Cadaver Inc./ex-Darkthrone/ex-Ulver/ex-Ved Buens Ende/ex-Fleurety/ex-Viod/ex-Inferno/ex-Virus (Norway)/ex-Satyricon/ex-White Willow/ex-Cadaver; drums), Kristian Eidskrem (ex-Hagalaz' Runedance/ex-Paradigma; bass), Svein Egil Hatlevik (a.k.a. Magic Logic/a.k.a.Zweizz; ex-Fleurety; keyboards/programming), Tom Kvålsvoll (a.k.a. Thrawn;ex-Nocturnal Breed/ex-Paradigma/ex-Esotreric; guitar), Yusuf Parvaz (a.k.a. Mr. Fixit/a.k.a.Vicotnik; ex-Ved Buens Ende/ex-Isengard/ex-Dimmu Borgir; guitars/drums). The former members featuring (at various times): Cerberus (bass), Ole Jørgen Moe (a.k.a. Apollyon; bass), Gylve Nagell (a.k.a. Fenriz; bass) and Jens F. Ryland (guitar).
Their discography has been much shorter than their membership list but is nonetheless impressive with Promo (1994), Kronet Til Konge (1995), Monumental Possession (1996), Satanic Art MCD (1998), 666 International (1999), with Satanic Art featuring Stine Lunde (violin)and Thomas Rune Andersen (a.k.a. Galder; guitar) as guest performers and Jonas Alver (a.k.a. Alver;: bass) on Monumental.