A hat is traditionally read as the role or idea you carry on your head — a mindset, a job, an identity. Changing hats in a dream is linked to switching between parts you play.
Has this come up in your dreams before? What was going on in your life then?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.