You need to tell the company to cancel your current direct debit and set up a new one on your joint account.
Most companies allow DDs to be set up online.
Monzo can’t move DDs around. All that happens in a Current Account Switch is Monzo tells the company to change the DD on your behalf, but you can’t use a switch to go from a sole account to a joint account.
Other banks allow sole accounts to be converted to joint accounts, meaning you could keep DDs as they are but I believe Monzo will open a new joint account.