Are any ocean fish vegetarian?

Certainly! Here are two sites which list quite a few.

https://micro.cornell.edu/research/epulopiscium/herbivory-fish
http://www.healthyreefs.org/cms/herbivorous-fish-abundance/

Aside from the truly carnivorous fish (like sharks) most fish are omnivorous. Some, like the parrotfish, may be said to eat both plants and animals, but their diet mostly consists of algae and aquatic plants.

Fish may also drastically change their diet during their life cycle. As an example, most species subsist on the plankton (which is comprised of both microscopic plants and animals) as a larva and then switch to different foods as they grow. Thus, a vegetarian fish may not be so over its entire lifetime.

Other marine animals such as manatees, dugongs, and sea turtles are truly vegetarian. Unlike these species, it is more difficult to lock fish into a specific category.