Final answer:
The exact number of Gold houses at the Institute and their names cannot be determined without specific context about the Institute or house system you are referring to.
Step-by-step explanation:
The number of Gold houses at the Institute and what they are named after is a key detail missing from your question. It appears you are referencing a specific work of fiction or a specific educational institution's house system, but without that context, I can only provide general information. Typically, house systems in schools are named after significant historical or mythological figures, such as Roman Emperors, Greek Titans, or gods from various pantheons.
As for the general background, the Greek pantheon includes Zeus and his siblings, as well as his children Hermes, Apollo, Artemis, and others. Meanwhile, the Roman pantheon includes gods like Jupiter, Venus, and Mercury, which were later used as names for planets in our Solar System. If the context is referring to Roman history, the number six could be associated with the six male Titans, or it could refer to the six days of creation in Christian lore if it is related to early Christianity.
Without the proper context of which Institute and system you are referring to, it's not possible to provide an accurate answer to how many Gold houses there are or what they are named after.