No, the chef decides what you’re going to eat. Because at that level, you pay for an original culinary experience, not to eat a well-cooked version of your favorite dish.

For example, at Sukiyabashi Jiro you get whatever the chef has prepared for the menu that today. Part of this is practical, the fish that will be used is usually purchased that very morning, and part of it is the quality of the restaurant. This isn't unique to Japan's concept of "choose to leave it to the chef" (omakase).

[0] https://www.sushi-jiro.jp/dining-at-jiro/