The Shifting Paradymes household contains the musically-inclined young adults Gunnar Roque, Jasmine Rai and Zoe Zimmerman, who are attending La Fiesta Tech. They appear to be a great band, yet they need practice and have never tried music before. They also seem to have arguments, which is referred to in one of their bios.
According to the picture on the neighborhood photos, Zoe plays the bass, Gunnar plays the electric guitar, and Jasmine plays the drums.
While they all have good relationships with one another, Gunnar has a better relationship with Jasmine than with Zoe.
They appear to have different ethnicities. Gunnar and Jasmine both have tattoos on their bodies and Gunnar's hair is black and done in a pony tail.
Their household name is most likely the name of their band name, the Shifting Paradymes.
The name probably refers to the idea of a "paradigm shift."