What is another name for fishbowl?

There isn't a single, widely-used synonym for "fishbowl." However, depending on the context, you could use one of these:

For a glass container:

* Aquarium

* Glass bowl

* Glass container

For a situation of intense scrutiny:

* Public eye

* Limelight

* Under a microscope

* The spotlight

For a metaphorical sense of transparency:

* Open book

* Crystal clear

* Transparent

The best synonym will depend on the specific context and meaning you want to convey.