bhakti-upadeśa - instruction of devotional service; vinu - without; tāṅra - His; nāhi - there is not; kārya - occupation; ataeva - therefore; nāma - the name; haila - became; advaita ācārya - the supreme teacher (ācārya) Advaita Prabhu.

Since He has no other occupation than to teach devotional service, His name is Advaita Ācārya.