Yes, that is the common name for this member of the cactus family that looks like it should be in the agave family.
Leuchtenbergia principis is from the Chihuahuan desert and unlike the agave it can bloom and bloom again, every year. Though they do not bloom young, so you may have to wait 10 years to see such a vibrant yellow flower.
Those weird papery spine things on the ends of the arm-like thingys are in fact the spines, true cactus spines, coming off the “arms” which are not branches or stems or even leaves, but what is a tubercule. Cactus are soooo interesting!
They need a tall pot, since they have a big and ruddy taproot.