O365: Outlook not able to set default signature for shared mailbox

Solution 1:

According to my experience, only the mailbox that configured mannually in your Outlook would be in the account list to set signature, and the auto-mapped shared mailbox would work with your primary maibox's signature.

In this case, if you need to set up a separate signaure for the shared mailbox, as a workaround, you could try to configure it in Outlook if it has a password.

If you don't like to configure it in Outlook, there may be other workarounds(such as add disclaimers on the server), for more information, please refer to this article:

How to set up different email signatures for a shared mailbox and user mailbox in Office 365?