Hi @LBoord,
The email signature cannot be added from this dropdown, you would change that in the Inbox Settings. Click Inbox Settings on the lower left of the screen (or navigate to Settings > Inbox > Inboxes).
Under Current view, make sure that you’re in the right inbox. Once you are, you should see your connected team email address. Hover your mouse over it, click Edit and you should see this:
This is where you can add a team signature. As far as I know, your individual signature cannot be used here, unless you save it as a snippet.
Hope this helps!