The Sanskrit word Sampradaya names a tradition and its teachings handed from Guru to guru in an unbroken stream (parampara). One enters a sampradaya by the diksha that belongs to that stream.
Within the International Nath Order that word names the older seats, not this house. The Adinath Sampradaya was a sadhu line. Mahendranath was its last guru. He would not give that diksha in the West. INO initiation is a householder transmission. This Order is cosmopolitan. It is not the Adinath or Uttara Kaula sampradaya under another name. Parampara and Guru stay pointed at Initiation. This page names the Sanskrit for a lineage-stream.