If you see something being covered with a blanket in a dream, it may signify protection and security. Being covered by something on all sides is a sign of comfort and assurance in waking life.
Also, dreaming about an uncovered box could mean not having anything to hide figuratively means stability, support.
Dreaming about being given a cover to conceal one’s private parts because one is ashamed to reveal them, then this might suggest shy personality traits in waking life or shame from past events.