Kalyanasundara Murthi is the lord Shiva himself. He is called as Kalyana Sundara Murthi at the time he gets married to Goddess Shakti, when she was in the form of Parvati.
Goddess Shakti, as Parvati Devi, was born to Parvata Raja. Parvata Raja is the one of the wealthiest kings on Earth. Parvati was in love with Lord Shiva and decides to marry him. For that, she wanted to go to Himalayas, wanted to perform austerity and do meditation in the fond remembrance of Lord Shiva. Lord Shiva was very pleased with her and wanted to test her admiration towards him. So he did come in the form of an old devotee and requested her for his rescue. Just the reason being the old man is the devotee of Lord Shiva, Parvati had saved him and offered him the Lunch and Dinner.
To test her devotion towards him, Lord Shiva in disguise had scolded himself and degraded her austerity. He also tries to convince her that instead of undergoing such tedious practice in the young age, she can marry a handsome guy and lead the life to the maximum. The old man tries to humiliate Lord Shiva by saying that he lives where the dead and evil forces stay together and she cannot spend her life there.
Just by listening to the old man, Parvati forces him to go away and she reconfirms that Lord Shiva is her would-be husband. Delighted with her reply and her dedication towards him, Lord Shiva comes to the original form followed by their Marriage at Parvata Raja’s residence.