cur.execute("INSERT INTO users_data (`user_id`, `name`) VALUES (%s, 'Канал %s');", (member.id, member.display_name,))
'Канал User_name'
, а 'Канал 'User_name''
. Это вызывает ошибкуpymysql.err.ProgrammingError: (1064, "You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'User_name'')' at line 1")