Hi Pbphut, Your Psychopsis Mariposa is beautiful!
Kinknstein is correct; the Psychopsis used to be considered an Oncidium, but was moved into its own genus a few years back.
As for your question about variety names, I'm thinking you are either asking about the names in small quotes, or the name following the term "var."
I will try my best to explain both.
For Psychopsis Mariposa (or just about any other orchid), there is the standard color form, that would be simply named Psychopsis Mariposa. There is also the alba form of this plant (I actually have one in my collection); alba being a different color form from the standard without any color pigment except yellow in this case. This would be named Psychopsis Mariposa var. alba (var. is the abbreviation for variety).
If you have a Psychopsis Mariposa that is a clone of either an awarded plant or one that someone cloned without an award, then it will carry the clonal name in small quotes after the plant name, such as in Psychopsis Mariposa 'Jill Sidran' AM/AOS.
To top it all off, you could have an alba form with a clonal name, which could be Psychopsis Mariposa var. alba 'Yellow Giant' HCC/AOS. (I made this last one up to show the example).
I hope this answers your questions without being too confusing.