Cómo resolver el ERROR 1060:Duplicar el nombre de la columna usando Vistas -> Crear vista

Utilice alias para asignar nombres:

CREATE VIEW v_payment AS
    SELECT p.payment_id, c.first_name as customer_first_name, c.last_name as customer_last_name,
           s.first_name as staff_first_name, s.last_name as staff_last_name,
           p.amount
    FROM payment p INNER JOIN
         customer c
         ON p.customer_ID = c.customer_ID INNER JOIN
         staff s
         ON p.staff_ID = s.staff_ID;

first_name y last_name aparecer dos veces en tu select lista. Lo anterior aclara si el nombre es para un cliente o personal.