The baddies in Edge of Tomorrow are black, amorphous tentacled creatures called Mimics. The problem is, as best as I can remember, they never actually mimic anything. And they certainly don't look like they're mimicking anything found on Earth. So who gave them that name, and why?
They were called mimics because they were capable of mimicking human military behavior extremely quickly. This happened to be a result of the Omega's time traveling capabilities, but the humans in the movie had no idea about that. All they knew was that they would attack one way, and the aliens immediately knew how to counter it or do it themselves.
Sky News Anchor: They appear to mimic and even anticipate our actions...
In Hiroshi Sakurazaka's All You Need is Kill, the novel upon which the movie was based, the Mimics are alien organisms (nanobots?) sent to "terraform" the earth to make it habitable for an alien race from a nearby star system.
Iirc, the "mimics" invaded native life (starfish) in order to co-opt their biology into a platform upon which they could build a bio-weapon, and were designed to adapt to their surroundings in order to accomplish their mission (including their ability to "loop back time" in order to anticipate dangers and other obstacles). They mimicked terran biology in order to adapt to the earth's environment, so that they could evolve and reproduce enough to begin transforming the earth into an environment more hospitable to their creators.
This ability to adapt is one reason they are called mimics.
It also appears that this may be a translation issue.
According to an answer I found on Quora, the original Japanese can be translated as "Gitai":
In that katakana form (ギタイ) it doesn't mean anything. It's just a name. But, it can be written in kanji as 擬態 (mimesis, mimicry, camouflage) or 義体 (artificial body, cyborg).