I shall answer your question about Christian Death-metal. It is called Death metal because the music style is similiar to not-Christian deathmetal. So is 'Doom'-metal. These style names are know by every metalhead on the world (Christian and not-Christian), so why should we make up new names as the style is already known as Deathmetal or Doommetal.

God Bless,

AscensioN- Christian death/doommetal band from Holland: http://www.wirehub.nl/~hammett4