Even Care is the one and only level of Petscop's overworld.
It is the home to the game's Pets.
“Even Care” might be an insult or joke nickname given to Care. If you consider the note in Care’s room, it talks about a child that goes to school and comes out crying “Nobody loves me!”. Something must have happened to her to make her react this way. If you consider that Care does not grow eyebrows, or that she obsessively plucks her own eyebrows, this would give school kids something to pick on her with. The word “even” is synonymous with featureless, like someone with no eyebrows. Without eyebrows, expressing emotion is very difficult, giving you a constant expression of boredom. This also relates to the Dr. Seuss story, where kids pick on Daisy-Head Mayzie because of her unique appearance.
It is also possible that "even" refers to a state of mind, Even Care referring the emotionally stable version of Care.
It can also be read as a question, as in "[Do you] even care?"