"Have you eaten your lunch" is the correct sentence because you have chosen a specific verb. The reader knows that you are talking about eating your lunch.

Correct => Structure of sentence => grammar => Both are correct ------------------------------------------------------------------------------------------------ Brett is right, Both are common I've had enough! In home Mother to Son: Have you eaten your breakfast yet? In a party ....to new guest: Have you had your dinner?

Both these sentences are correct; they have the same meaning. Both are commonly used.