Swaminarayan's birth name was Ghanshyam. So why he is called Nilkanth?
At the age of 11, after the death of Ghanshyam's parents, he left his home to travel whole India. His 7 years journey focused on reestablishing the ideals of Hindu Sanatan Dharma. He took the name Neelkanth Varni while on his journey. After he met Ramanand Swami, Ramanand Swami gave him diksha and renamed him Narayan Muni and Sahajanand Swami. Later he is known as Lord Swaminarayan.
Source: Teenage Yogi - Neelkanth Varni
When Dharma-Dev and Bhaktimata (Ghanshyam's parents) asked Markandeya Rishi to name Ghanshyam, he predicted that Ghanshyam would be known as Nilkanth throughout the world. Later, when he left home after his parent's death to travel, he was known as Nilkanth Varni.