You should have name column as a unique constraint. here is a 3 lines of code to change your issues
First find out the primary key constraints by typing this code
\d table_name
you are shown like this at bottom "some_constraint" PRIMARY KEY, btree (column)
Drop the constraint:
ALTER TABLE table_name DROP CONSTRAINT some_constraint
Add a new primary key column with existing one:
ALTER TABLE table_name ADD CONSTRAINT some_constraint PRIMARY KEY(COLUMN_NAME1,COLUMN_NAME2);
That's All.