"Red Giant" is actually a category of stars, describing a stage in their life cycle. Many different stars become red giants, and each one has its own unique name.
Examples of red giant stars:
* Betelgeuse (in the constellation Orion)
* Arcturus (the brightest star in the constellation Boötes)
* Mira (in the constellation Cetus)
So, while "red giant" is a description, not a name, it's an important one that tells us about a star's size, temperature, and evolutionary stage.