can someone tell me the name of a Mexican dish?!

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That doesn't sound Mexican at all. It sounds like grilled chicken on a bed of rice with white cheese dip on top. People don't eat white cheese dip in Mexico, only the orange colored one, and that is for potato chips not chicken.
In Mexico this would be called pollo a la parrilla or pollo a la plancha. If it is chicken breast it might be called pechuga a la parrilla or pechiga a la plancha. In Mexico it is is customary to serve the rice before the main course.
This is not an authentic Mexican dish.

I live and eat Mexican food in Mexico

this sounds to me like an American version of Aroz con Pollo con salsa de queso. Chicken and rice with a cheese topping, exactly as you described it.

My Mom used to make a dish years ago.it was called.Spanish Rice. Recipe :
Hamburger Meat scrambled in a skillet.when meat is cooked, add tomato sauce,can of tomatoes,mix well.Add cooked rice.Delicious.
optional :diced bell peppers added to the hamburger meat while cooking.

Mom's Recipe.

It might be 'paella'.