Hmm, I can’t think of an anime that matches the trailer. That is to say, an anime that is an action-horror demon-world adventure with modern military weapons.
Hole in the ground with horror monsters makes me think of Made in Abyss.
There’s a gluttony of anime with monsters in dungeons, like DanMachi, Arifureta, and Solo Leveling.
There’s Chained Soldier, which technically takes place in a hell-ish place with monsters that is connected to regular earth. And there’s some military element to it.
There’s a gate to another world and modern military in Gate: Thus the JSDF Fought There!, but no monsters that I recall.
Just throwing some other out there: Hellsing Ultimate, Seraph of the End, WorldEnd, Dimension W, .
When I hear arctic demon, I can’t help but think about The Thing, which isn’t anime.
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This is called localization.
Information or brevity will always be lost in translation (and communication in general), so the translator needs to pick what information to convey and how to convey it. Sometimes it can be difficult to find a satisfactory localized translation, like translating a pun. Or if the translation has been localizing the Japanese name-honorifics system as whatever the characters in an English speaking country would call each other, but then there is a long dialogue in the show discussing how they are addressing each other; that dialogue can throw a wrench in the translation.
For Love is War, the source joke word was probably ちんちん (chinchin) which is both a childish way to say “penis” (like “poopoo” is a childish way to say 💩, or like “peepee”) and a dog trick where the dog sits and begs (it might also have additional meanings). The translator probably had to think about how to make a similar gag with the existing visuals.