Is is called a cocktail dinner or and dinner?

It's called a cocktail party, not a cocktail dinner.

Here's the difference:

* Cocktail party: A social gathering where guests mingle and socialize while standing and eating small, finger foods and drinking cocktails.

* Dinner party: A more formal event where guests sit at a table to eat a multi-course meal.

It's possible to have a cocktail dinner, but it's less common. This would mean a dinner party where guests enjoy cocktails before the meal, but the main focus is still on the sit-down dinner.