Tri – three, Yugi – Yuga, Narayan – a name of Vishnu.
In Triyuginarayan in the Himalayas Shiva and Parvati married. Brahma was the priest, Vishnu was the witness.
Since the marriage in Satya Yuga an eternal (akhand) fire (Dhuni) is burning in the temple, that is called Akhand Dhuni Temple.
Recommendation for reading: Parvati Mangala of Tulsidas