iOS: Choose "Lists" at the top left in your shopping list. Tap on the 3 dots on the right side of the list that you want to rename and choose "Rename". Alternatively, you can swipe to the left and choose "Rename".
Android: Choose the list symbol at the top right in your shopping list. Tap on the 3 dots on the right side of the list that you want to rename and choose "Rename".