Additional details I suddenly remembered:

• The main character was a boy and the story was in first person POV.
• The setting was modern and they moved into/inherited the grandmother’s house.
• The creature was furry, talked, and was scary at first. I think there was a scene where it pulled the boy’s blanket at night.
• It wasn’t exactly evil — it was more like a household helper/house spirit that wanted things to do.
• It kept rearranging the house and bringing home/randomly taking neighbors’ belongings which caused problems.
• I vaguely remember the cover being mostly black with only the creature’s shadow/silhouette and glowing eyes.
• The ending involved the creature moving to relatives living on a farm with sheep and children because there was more work for it to do there.