Shiva is called as Hiranyareta because he possesses very graceful and pleasing luster. Shiva is the cause of graceful and pleasing creation. Sadashiva alone gives rise to knowledge for the benefit of the world. He never harms anyone and he never spoils anything. The annihilation is actually a process to shape a new creation.
Gold is also said as Hiranya in Sanskrit. Its luster is highly pleasing. Gold is mentioned as the semen of Lord Shiva in the Puranas. Therefore Shiva is called as Hiranyareta.
One name of fire is also Hiranyareta. There is a deity called Agnimoorty among the eightfold deity of the Lord. Shiva is said to be Hiranyareta for possessing the form of Agnimoorty. The gorgeous beauty of Rambha was based on the Hiranyareta nature of Agni (fire) and this story is elaborately described in Brahma-Vaivarta-Purana. Aalwal defines this name as under—

त्वद्वीर्ययोगेन भवेद्धिरण्यं यद्वाग्निरूपोऽस्यथ वा जलार्धे।
त्यक्तेन वीर्येण बभूव हैममण्डं तदीशासि हिरण्यरेताः॥

Purport: O Lord! The gold is made out of contact with your luster. You are called as Hiranyareta due to your fiery-form. Otherwise you are called as Hiranyareta because your semen was ejaculated in the water by which this golden universe came into existence.
According to Saur-Sanhita of Skanda-Purana, In the beginning of creation Shiva dropped his goldenizing semen in the water element, which was eventually turned into the form of universe. As per Ayur-Veda, mercury is nothing but the semen of Lord Shiva. The gold was made out of alchemical refining of mercury. For this reason, Shiva is known as Hiranyareta. Wherever we find some brightness, that belongs to Shiva only, keeping such an understanding is the true sense of worship of Hiranyareta.