You can create a new emblem for your Den by selecting its patterns, frames, and symbols as well as the colors that you would like to see for each.

During Den creation, tap the "Edit Emblem" button.

You can also create a random emblem by tapping the "random" button.

If you want to change your existing emblem, you must be the Leader. Go to the drop-down menu next to the Den's name in the member's list, then choose Den Settings.