What is our universe called?
Other than "The Universe", it has no name.
Until the early 20th Century, it was widely thought that our universe consisted only of our own galaxy, the milky way (Galaxy is from the Greek word for milk, so actually "Galaxy" means milky way!). At that time, the terms "Galaxy" and "Universe" were used almost interchangeably.
Once it was discovered that objects called "spiral nebula" were in fact other galaxies millions of light years away (thanks to the groundbreaking work of Henrietta Swan Leavitt, which provided the tools for Edwin Hubble to make the discovery), other galaxies were sometimes referred to as "island universes".
Over the next decades, the current terminology came in to use, with Milky Way as the name of our galaxy, the term Galaxy for all galaxies (groupings of billions of stars gravitationally bound), and Universe for everything.