By default, Laravel does not require a primary key on many-to-many tables. The relationship will work just fine without it.
But there are reasons you might still want to add one. For example, I was recently helping someone migrate from a single instance of MySQL to a managed MySQL cluster provided by Digital Ocean.
While not 100% required, they strongly recommend that every table has a primary key, in order to improve the reliability and performance of replication between database nodes.
No special configuration is needed in Laravel to enable the primary key, other than adding a column with a migration using $table->id(). You can do this when originally creating the table or you can add it later, perhaps after reading this tip.
Here to help,
Joel
P.S. Would you like some help moving your database onto more resilient infrastructure? Let's talk!