There isn't a single, universally accepted name for a blue and red rock. This is because the colors you describe could be caused by various minerals, rock types, and geological processes.

Here are some possibilities, depending on the specific combination of blue and red:

* Jasper: Jasper is a variety of chalcedony that can come in a wide range of colors, including red, brown, yellow, and blue. Some jaspers have a combination of red and blue, often with swirls or bands.

* Agate: Agate is another variety of chalcedony, known for its banded patterns. Some agates have blue and red banding, creating a visually striking effect.

* Rhyolite: Rhyolite is an igneous rock that can be red, pink, or even blue, depending on the minerals present.

* Quartzite: Quartzite is a metamorphic rock formed from sandstone. Depending on the impurities present, quartzite can have red, blue, or even green hues.

To give you a more accurate answer, I would need more information about the rock, such as:

* Where did you find it? Location can help identify the type of rock.

* What is the texture? Is it smooth, rough, or layered?

* How hard is it? Can you scratch it with a fingernail or a coin?

If you can provide more information, I might be able to give you a better idea of what kind of rock you have.