It depends on which client you're using, but on the web:
1. Open the board.
2. Click on the board name itself (in the upper left).
3. A rename popup should appear.
This only works if you're an admin on the board - that'll be true if you created the board, or someone else added you as an admin.
In addition to Dan's answer, if you are on an iOS device (probably similar for Android as well), if you:
1. Tap on the "..." symbol in the upper right of the board view
2. Tap on the gear icon in the upper right
3. Tap on the 'Name' field and edit the name of the board
that should rename the board on mobile.
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