In countries such as the U.S. It is known as a garbage container in the United States and Canada, which seems logical given the nature of its use. However, in the UK we call them containers (or containers for containers in Australia). The most accepted explanation has its origin in the ancient art of beekeeping.
What about the trash can? I was called that once because I ate a lot of food. In fact, there wasn't much food. At least, that's the term I grew up with on my parents' farm. It's the closest equivalent I could find to a British container.
In fact, it's called a dump. The huge containers where garbage bags are deposited are also known as garbage containers. What do they call those huge garbage cans in the UK?.