He was from the branch family of the Adachi clan and Nagayasu started to use the name Osone which was derived from his father's territory, Osone manor (Yamagata City), so he was also called Nagayasu OSONE.
安達氏の庶家で、長泰から父の所領大曾禰荘（山形市）を由来とした大曾禰を名字とし、大曾禰長泰とも称される。