With Japanese restaurants where I do omakase, I do try to let them know what I've had before (and what I've liked/disliked).

There are a few restaurants where I will go once a season for the chef's tasting menu, but then not really go back until the next seasonal menu change.

For a few restaurants, I've actually used the tasting menu to get a sense of whether I like to the style and preparation of a chef before I go back for an a la carte meal. Though sometimes I'll rebel and just build my own tasting menu if I don't like theirs...